Teacher edition (with key)← High School Math 1

High School Math 1 — every item

NC Math 1 (18 chapters) · 140 items

One section per unit, in course order. For review and for a year of homework sheets.

01Exponentslaws-of-exponents

1.
Evaluate $8^{2/3}$ .
Answer: ______________
2.
Simplify $\dfrac{12x^{-3}y^{4}}{4x^{2}y^{-1}}$ . Write the result with positive exponents only.
Answer: ______________
3.
Light travels at $3 \times 10^{8}$ metres per second. The Sun is $1.5 \times 10^{11}$ metres from Earth. How many seconds does sunlight take to reach Earth?
Answer: ______________
4.
Which is the value of $\left(2^{3} \cdot 2^{-5}\right)^{2}$ ?
1. (A)
  $-16$
2. (B)
  $1$
3. (C)
  $\dfrac{1}{16}$
4. (D)
  $2^{-30}$
5.
If $\dfrac{4^{10} \cdot 8^{5}}{16^{6}} = 2^{n}$ , what is $n$ ?
1. (A)
  $5$
2. (B)
  $9$
3. (C)
  $10$
4. (D)
  $11$
5. (E)
  $35$

02Algebraic expressions (Math 1)algebraic-expressions-m1

1.
In the expression $7x^{2} - 4x + 9$ , what is the coefficient of $x$ ?
Answer: ______________
2.
Simplify $2(3x - 4) - 5x$ .
Answer: ______________
3.
Evaluate $4x^{2} - 6x + 1$ when $x = \dfrac{1}{2}$ .
Answer: ______________
4.
Which expression means “twice the sum of a number $x$ and $3$ , decreased by $5$ ”?
1. (A)
  $2x + 3 - 5$
2. (B)
  $2(x - 5) + 3$
3. (C)
  $2(x + 3) - 5$
4. (D)
  $5 - 2(x + 3)$
5.
A rectangular garden has width $w$ feet. Its length is $4$ feet more than three times its width. Which expression gives the perimeter of the garden, in feet?
1. (A)
  $4w + 4$
2. (B)
  $8w + 8$
3. (C)
  $6w + 8$
4. (D)
  $3w^{2} + 4w$

03Polynomialspolynomial-operations

1.
Classify $4x^{3} - 2x + 7$ by its number of terms and its degree.
1. (A)
  binomial, degree $3$
2. (B)
  trinomial, degree $3$
3. (C)
  trinomial, degree $2$
4. (D)
  trinomial, degree $7$
2.
Expand and simplify $(2x - 3)(x + 5)$ .
Answer: ______________
3.
A rectangle has length $x + 6$ and width $x + 2$ . Its area, expanded, is $x^{2} + bx + c$ . What is $b$ ?
Answer: ______________
4.
Which is the expansion of $(x + 5)^{2}$ ?
1. (A)
  $x^{2} + 25$
2. (B)
  $x^{2} + 5x + 25$
3. (C)
  $x^{2} + 10x + 25$
4. (D)
  $x^{2} + 10x + 10$
5.
Real numbers $x$ and $y$ satisfy $x + y = 7$ and $xy = 10$ . What is $x^{2} + y^{2}$ ?
1. (A)
  $19$
2. (B)
  $29$
3. (C)
  $39$
4. (D)
  $49$
5. (E)
  $69$

04Equations and inequalities (Math 1)multi-step-equations-literals

1.
Solve $5x - 7 = 3x + 9$ .
Answer: ______________
2.
The area of a triangle is $A = \dfrac{1}{2}bh$ . Solve for $h$ . Enter your answer as an equation beginning with $h =$ .
Answer: ______________
3.
How many solutions does $3(2x - 1) + 4 = 6x + 1$ have?
1. (A)
  no solution
2. (B)
  exactly one solution, $x = 0$
3. (C)
  exactly one solution, $x = 1$
4. (D)
  infinitely many solutions
4.
Which describes all solutions of $-3 < 2x + 1 \le 7$ ?
1. (A)
  $x < -2$ or $x \ge 3$
2. (B)
  $-2 < x \le 3$
3. (C)
  $-1 < x \le 4$
4. (D)
  $-2 \le x < 3$
5.
The equation $a(x - 2) = 3x + b$ has infinitely many solutions. What is $a + b$ ?
1. (A)
  $-9$
2. (B)
  $-6$
3. (C)
  $-3$
4. (D)
  $3$
5. (E)
  $9$

05Linear equations and inequalities (two variables)linear-forms-half-planes

1.
What is the slope of the line $3x + 4y = 12$ ?
Answer: ______________
2.
Write the equation of the line through $(2, -1)$ that is perpendicular to $y = 2x + 4$ . Give it in slope-intercept form, as an equation beginning with $y =$ .
Answer: ______________
3.
A line passes through $(1, 5)$ and $(4, -4)$ . What is its $y$ -intercept?
Answer: ______________
4.
The inequality $y < 2x - 3$ is graphed with a dashed boundary line and one half-plane shaded. Which point lies in the shaded region?
1. (A)
  $(0, 0)$
2. (B)
  $(1, 2)$
3. (C)
  $(2, 1)$
4. (D)
  $(3, 1)$
5.
A line is parallel to $4x - 3y = 9$ and passes through $(6, 1)$ . What is the $y$ -intercept of this line?
Answer: ______________

06Systems of equations and inequalitieslinear-systems

1.
Solve the system by substitution and enter $x$ :

$y = 2x - 1, \qquad 3x + y = 14$
Answer: ______________
2.
Solve the system by elimination and enter $y$ :

$3x + 2y = 16, \qquad 5x - 4y = 1$
Answer: ______________
3.
A school play sells $120$ tickets. Adult tickets cost $8 and student tickets cost $5, and the total collected is $780. How many adult tickets were sold?
Answer: ______________
4.
How many solutions does this system have?

$2x - 4y = 8, \qquad x - 2y = 6$
1. (A)
  exactly one solution
2. (B)
  no solution
3. (C)
  infinitely many solutions
4. (D)
  exactly two solutions
5.
Three pens and two notebooks cost $11. Two pens and three notebooks cost $14. What is the cost of one pen and one notebook together?
1. (A)
  $1
2. (B)
  $3
3. (C)
  $4
4. (D)
  $4.50
5. (E)
  $5

07Relations and functionsfunction-foundations

1.
If $f(x) = 3x - 5$ , find $f(4)$ .
Answer: ______________
2.
Let $f(x) = \dfrac{x + 4}{2}$ . Find the value of $x$ for which $f(x) = 11$ .
Answer: ______________
3.
Which relation is a function?
1. (A)
  $\{(1, 2),\ (2, 3),\ (1, 4)\}$
2. (B)
  $\{(0, 1),\ (0, 2),\ (0, 3)\}$
3. (C)
  $\{(2, 1),\ (2, 3),\ (3, 4)\}$
4. (D)
  $\{(1, 2),\ (2, 2),\ (3, 2)\}$
4.
What is the domain of $f(x) = \sqrt{x - 1}$ , in interval notation?
1. (A)
  $(-\infty, \infty)$
2. (B)
  $[1, \infty)$
3. (C)
  $(1, \infty)$
4. (D)
  $[0, \infty)$
5.
The function $C(m) = 25 + 0.15m$ gives the cost in dollars of renting a van and driving it $m$ miles. For how many miles driven is the cost $61?
Answer: ______________

08Factoring polynomialsfactoring-polynomials

1.
Which is the complete factorization of $12x^{3} - 18x^{2}$ ?
1. (A)
  $6x(2x^{2} - 3x)$
2. (B)
  $3x^{2}(4x - 6)$
3. (C)
  $2x^{2}(6x - 9)$
4. (D)
  $6x^{2}(2x - 3)$
2.
Factor $6x^{2} - 5x - 6$ completely.
Answer: ______________
3.
A rectangle has area $x^{2} + 7x + 12$ square units and width $x + 3$ units. Write an expression for its length.
Answer: ______________
4.
Factor $x^{2} - 9$ .
1. (A)
  $(x - 3)^{2}$
2. (B)
  $(x + 3)^{2}$
3. (C)
  $(x - 3)(x + 3)$
4. (D)
  $(x - 9)(x + 1)$
5.
The trinomial $x^{2} + bx + 48$ can be factored as $(x + p)(x + q)$ , where $p$ and $q$ are positive integers. How many different values of $b$ are possible?
1. (A)
  $4$
2. (B)
  $5$
3. (C)
  $6$
4. (D)
  $8$
5. (E)
  $10$

09Quadratic equations and functionsquadratics-parabolas

1.
Solve $x^{2} - 5x + 6 = 0$ . Enter the larger solution.
Answer: ______________
2.
Solve $2x^{2} - 3x - 2 = 0$ using the quadratic formula. Enter the negative solution.
Answer: ______________
3.
A ball is thrown upward from a platform. Its height in feet after $t$ seconds is $h(t) = -16t^{2} + 64t + 80$ . What is the maximum height the ball reaches, in feet?
Answer: ______________
4.
What is the $x$ -coordinate of the vertex of $y = 3x^{2} - 12x + 7$ ?
1. (A)
  $-2$
2. (B)
  $2$
3. (C)
  $6$
4. (D)
  $12$
5.
The two real roots of $x^{2} - 7x + k = 0$ differ by $3$ . What is $k$ ?
1. (A)
  $4$
2. (B)
  $6$
3. (C)
  $8$
4. (D)
  $10$
5. (E)
  $12$

10Exponential functionsexponential-growth-decay

1.
Let $f(x) = 800(0.5)^{x}$ . Find $f(3)$ .
Answer: ______________
2.
A car bought for $24,000 loses $15\%$ of its value each year. What is its value after $2$ years, in dollars?
Answer: ______________
3.
A table gives $x = 0, 1, 2, 3$ and $y = 3, 6, 12, 24$ . Which function matches the table?
1. (A)
  $y = 2 \cdot 3^{x}$
2. (B)
  $y = 3x + 3$
3. (C)
  $y = 3 \cdot 2^{x}$
4. (D)
  $y = 6^{x}$
4.
Which situation is modelled by an exponential function?
1. (A)
  A bacteria count doubles every hour
2. (B)
  A plant grows $2$ cm each week
3. (C)
  A taxi charges $2 per mile
4. (D)
  A savings jar gains $2 every month
5.
$2,000 is deposited in an account paying $6\%$ annual interest, compounded semi-annually. What is the balance after $1$ year, in dollars, to the nearest cent?
Answer: ______________

11Graphing functionsfunction-features

1.
A piecewise function is defined by

$f(x) = \begin{cases} x + 3 & \text{if } x < 0 \\ 2x & \text{if } x \ge 0 \end{cases}$

Find $f(-2)$ .
Answer: ______________
2.
Let $f(x) = x^{2} - 2x$ . Find the average rate of change of $f$ from $x = 1$ to $x = 4$ .
Answer: ______________
3.
A graph starts at $(-4, 2)$ , falls to a low point at $(-1, -3)$ , rises to a high point at $(2, 5)$ , then falls to its end at $(5, 0)$ . On which interval is the function increasing?
1. (A)
  $(-1, 2)$
2. (B)
  $(-4, -1)$
3. (C)
  $(2, 5)$
4. (D)
  $(-3, 5)$
4.
The table gives the height $h(t)$ , in metres, of a drone $t$ seconds after launch.

$t$ $0$ $2$ $5$
$h(t)$ $12$ $20$ $44$

What is the average rate of change of $h$ from $t = 2$ to $t = 5$ , in metres per second?
1. (A)
  $24$
2. (B)
  $8$
3. (C)
  $\dfrac{32}{3}$
4. (D)
  $6.4$
5.
What is the maximum value of the function $f(x) = -x^{2} + 6x - 5$ ?
Answer: ______________

$t$	$0$	$2$	$5$
$h(t)$	$12$	$20$	$44$

12Comparing functionscomparing-function-families

1.
A table gives $x = 0, 1, 2, 3$ and $y = 2, 5, 10, 17$ . Which family does the table belong to?
1. (A)
  Quadratic
2. (B)
  Linear
3. (C)
  Exponential
4. (D)
  None of these
2.
A table gives $x = 0, 1, 2, 3$ and $y = 4, 12, 36, 108$ . The pattern continues. What is $y$ when $x = 5$ ?
Answer: ______________
3.
Let $L(x) = 20x$ and $E(x) = 2^{x}$ . For small positive $x$ , $L(x)$ is larger. What is the smallest positive integer $x$ for which $E(x) > L(x)$ ?
Answer: ______________
4.
A table gives $x = 1, 2, 3, 4$ and $y = 5, 8, 11, 15$ . Which statement about the table is correct?
1. (A)
  Linear, because the differences are all about $3$
2. (B)
  Exponential, because $y$ keeps increasing
3. (C)
  Not linear, because the first differences $3, 3, 4$ are not all equal
4. (D)
  Quadratic, because the second differences are $0$ and $1$
5.
A quadratic function $f$ satisfies $f(0) = 3$ , $f(1) = 6$ , and $f(2) = 13$ . What is $f(5)$ ?
1. (A)
  $43$
2. (B)
  $48$
3. (C)
  $53$
4. (D)
  $58$
5. (E)
  $63$

13Patterns, sequences, and seriesarithmetic-geometric-sequences

1.
An arithmetic sequence begins $7, 11, 15, 19, \dots$ What is its $20$ th term?
Answer: ______________
2.
A sequence begins $-2, 3, 8, 13, \dots$ Write an explicit formula for its $n$ th term. Enter just the expression for $a_n$ in terms of $n$ .
Answer: ______________
3.
A ball is dropped and each bounce rises to $\dfrac{3}{4}$ of the height of the previous bounce. The first bounce reaches $48$ cm. How high, in cm, does the fourth bounce reach?
Answer: ______________
4.
What is the $15$ th term of the arithmetic sequence $50, 44, 38, 32, \dots$ ?
1. (A)
  $-40$
2. (B)
  $-28$
3. (C)
  $-34$
4. (D)
  $134$
5.
The sum of the first $n$ terms of the arithmetic sequence $5, 8, 11, 14, \dots$ is $440$ . What is $n$ ?
1. (A)
  $14$
2. (B)
  $15$
3. (C)
  $16$
4. (D)
  $17$
5. (E)
  $18$

14Polygonspolygons-angle-theorems

1.
What is the sum of the interior angles of a hexagon, in degrees?
Answer: ______________
2.
What is the measure of each interior angle of a regular $12$ -gon, in degrees?
Answer: ______________
3.
Each interior angle of a regular polygon measures $156^\circ$ . How many sides does the polygon have?
Answer: ______________
4.
Which statement about quadrilaterals is true?
1. (A)
  Every square is a rhombus
2. (B)
  Every rectangle is a rhombus
3. (C)
  No rhombus is a rectangle
4. (D)
  Every parallelogram is a rectangle
5.
The interior angles of a convex hexagon, in degrees, form an arithmetic sequence with common difference $10$ . What is the measure of the largest angle, in degrees?
1. (A)
  $115$
2. (B)
  $125$
3. (C)
  $135$
4. (D)
  $145$
5. (E)
  $155$

15Coordinate geometrycoordinate-geometry

1.
Find the distance between $(-2, 3)$ and $(4, 11)$ .
Answer: ______________
2.
Point $P$ lies on the segment from $A(1, 2)$ to $B(9, 14)$ so that $AP : PB = 1 : 3$ . What is the $y$ -coordinate of $P$ ?
Answer: ______________
3.
A triangle has vertices $(1, 1)$ , $(7, 3)$ , and $(3, 6)$ . What is its area, in square units?
Answer: ______________
4.
What is the midpoint of the segment joining $(-5, 2)$ and $(3, 8)$ ?
1. (A)
  $(-1, 5)$
2. (B)
  $(-2, 10)$
3. (C)
  $(4, 3)$
4. (D)
  $(-4, -3)$
5.
Triangle $ABC$ has vertices $A(1, 2)$ , $B(7, 2)$ , and $C(7, 10)$ . What is the length of the median from $B$ to side $\overline{AC}$ ?
1. (A)
  $\sqrt{13}$
2. (B)
  $4$
3. (C)
  $5$
4. (D)
  $\sqrt{34}$
5. (E)
  $\sqrt{41}$

16Euclidean geometry: transformations and congruencetransformations-congruence

1.
The point $(3, -2)$ is rotated $90^\circ$ counter-clockwise about the origin. Enter the $x$ -coordinate of the image.
Answer: ______________
2.
A vertex $P(-4, 6)$ of a triangle is rotated $90^\circ$ counter-clockwise about the origin, and the result is then dilated by a scale factor of $\dfrac{1}{2}$ about the origin. Enter the $y$ -coordinate of the final image.
Answer: ______________
3.
A single transformation maps $A(2, 5)$ to $A'(5, 2)$ and $B(-1, 3)$ to $B'(3, -1)$ . Which transformation is it?
1. (A)
  Reflection over the $x$ -axis
2. (B)
  Rotation of $90^\circ$ counter-clockwise about the origin
3. (C)
  Translation by $(3, -3)$
4. (D)
  Reflection over the line $y = x$
4.
Two triangles share some equal measurements. Which set of equal parts guarantees the triangles are congruent?
1. (A)
  Two sides and a non-included angle
2. (B)
  Three angles
3. (C)
  Two sides and the included angle
4. (D)
  One side and one angle
5.
A triangle has vertices $(1, 1)$ , $(5, 1)$ , and $(1, 4)$ . It is dilated by a scale factor of $3$ about the origin. What is the perimeter of the image, in units?
Answer: ______________

17Statistics: center and spreaddescriptive-stats-spread

1.
Find the mean of $4,\ 7,\ 7,\ 10,\ 12$ .
Answer: ______________
2.
Find the population standard deviation $\sigma$ of $5,\ 7,\ 8,\ 9,\ 11$ .
Answer: ______________
3.
Eight runners' times, in minutes: $14,\ 15,\ 16,\ 18,\ 20,\ 21,\ 22,\ 40$ . Using the $1.5 \times IQR$ rule, what is the upper fence (the value above which a time counts as an outlier)?
Answer: ______________
4.
Six quiz scores are $7,\ 9,\ 9,\ 10,\ 12,\ 13$ . Their mean is $10$ . What is the population standard deviation $\sigma$ ?
1. (A)
  $2$
2. (B)
  $4$
3. (C)
  $\sqrt{24}$
4. (D)
  $24$
5.
A data set has mean $40$ and standard deviation $5$ . Every value in the set is doubled. What are the mean and standard deviation of the new data set?
1. (A)
  mean $80$ , standard deviation $5$
2. (B)
  mean $40$ , standard deviation $10$
3. (C)
  mean $80$ , standard deviation $20$
4. (D)
  mean $80$ , standard deviation $10$

18Data analysis: two variablesbivariate-regression

1.
A survey asked students how they get to school.

Bus Walk
Grade 6 $18$ $12$
Grade 7 $24$ $6$

What percent of the grade 7 students walk? Enter the number only.
Answer: ______________
2.
A line of best fit is $\hat y = 2.5x + 10$ . One data point is $(6, 22)$ . What is the residual for this point?
Answer: ______________
3.
For a class, the line $\hat y = 3.2x + 15$ predicts a test score $y$ from hours of study $x$ . Which is the best interpretation of the number $3.2$ ?
1. (A)
  The predicted score for a student who studies $0$ hours
2. (B)
  The correlation between study time and score
3. (C)
  Each additional hour of study predicts about $3.2$ more points
4. (D)
  Every student's score rises exactly $3.2$ points per hour
4.
In a study of elementary-school children, shoe size and reading score have correlation $r = 0.2$ . Which statement is the best conclusion?
1. (A)
  There is a strong positive relationship, so bigger feet cause better reading
2. (B)
  There is a weak positive association; something else, such as age, could explain both
3. (C)
  Since $r > 0$ , $20\%$ of a child's reading score is explained by shoe size
4. (D)
  There is no association, because $r$ is less than $0.5$
5.
A line is fitted to data on a plant's height over $30$ days. In the residual plot, the residuals are positive for the first $8$ days, negative from day $9$ to day $22$ , and positive again after day $22$ , forming a U-shaped curve. Which conclusion is best?
1. (A)
  A linear model is not appropriate; the curved pattern means the relationship is not linear
2. (B)
  The linear model fits well because the residuals are both positive and negative
3. (C)
  The correlation $r$ must be exactly $0$
4. (D)
  The slope of the fitted line must be negative

	Bus	Walk
Grade 6	$18$	$12$
Grade 7	$24$	$6$

undefinedWhole numbers: primes, GCF, and LCMgcf-lcm-grade6

1.
Write $84$ as a product of primes. How many distinct prime factors does it have?
Answer: ______________
2.
Using $84 = 2^2 \cdot 3 \cdot 7$ and $120 = 2^3 \cdot 3 \cdot 5$ , find $\text{GCF}(84, 120)$ .
Answer: ______________
3.
Using $84 = 2^2 \cdot 3 \cdot 7$ and $120 = 2^3 \cdot 3 \cdot 5$ , find $\text{LCM}(84, 120)$ .
Answer: ______________
4.
Two buses leave the depot together at 8:00. Bus A leaves every $12$ minutes and Bus B every $18$ minutes. When do they next leave together?
1. (A)
  8:06
2. (B)
  8:30
3. (C)
  8:36
4. (D)
  11:36
5.
A ribbon $84$ cm long and a ribbon $120$ cm long are each cut into pieces of the same length, as long as possible, with nothing left over. How many pieces are there in total?
1. (A)
  12
2. (B)
  17
3. (C)
  24
4. (D)
  204
5. (E)
  840

undefinedFractions: division and multi-step storiesfraction-operations-6

1.
$\dfrac{1}{2} \div \dfrac{1}{8} = \ ?$
1. (A)
  $\dfrac{1}{16}$
2. (B)
  $\dfrac{1}{4}$
3. (C)
  $4$
4. (D)
  $16$
2.
Compute $3\dfrac{1}{2} \div \dfrac{3}{4}$ . Give your answer as a fraction or mixed number.
Answer: ______________
3.
A jug holds $6$ cups of juice. How many $\dfrac{3}{4}$ -cup servings can be poured from it?
Answer: ______________
4.
Compute $2\dfrac{2}{3} \times 1\dfrac{1}{2}$ .
Answer: ______________
5.
Mia spent $\dfrac{2}{5}$ of her money on a book, then $\dfrac{1}{3}$ of the remainder on lunch. She had $24 left. How much money did she start with, in dollars?
Answer: ______________

undefinedDecimals: terminating and repeatingdecimals-terminating-repeating

1.
Write $\dfrac{7}{8}$ as a decimal.
Answer: ______________
2.
Which fraction has a terminating decimal?
1. (A)
  $\dfrac{1}{3}$
2. (B)
  $\dfrac{1}{6}$
3. (C)
  $\dfrac{1}{8}$
4. (D)
  $\dfrac{1}{9}$
3.
Compute $4.2 \times 0.35$ .
Answer: ______________
4.
Compute $7.2 \div 0.08$ .
Answer: ______________
5.
The decimal form of $\dfrac{3}{11}$ repeats. Enter the two-digit block that repeats.
Answer: ______________

undefinedNegative numbers and absolute valueintegers-absolute-value

1.
A submarine is at an elevation of $-250$ metres. How far is it from the surface, in metres?
Answer: ______________
2.
Which list is in order from least to greatest?
1. (A)
  $-\dfrac{3}{2},\ -2,\ -2.5,\ 0,\ \dfrac{1}{2}$
2. (B)
  $0,\ \dfrac{1}{2},\ -\dfrac{3}{2},\ -2,\ -2.5$
3. (C)
  $-2.5,\ -2,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
4. (D)
  $-2,\ -2.5,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
3.
At 6 a.m. the temperature was $-7^\circ$ C. At noon it was $-3^\circ$ C. Which statement is correct?
1. (A)
  $-7 > -3$ , so 6 a.m. was warmer.
2. (B)
  $-3 > -7$ , so noon was warmer.
3. (C)
  $\lvert -7 \rvert < \lvert -3 \rvert$ , so 6 a.m. was warmer.
4. (D)
  Both are below $0$ , so they are equally cold.
4.
Compute $\lvert -4 \rvert + \lvert 3 \rvert - \lvert -2 \rvert$ .
Answer: ______________
5.
On a number line, point $A$ is at $-6$ and point $B$ is at $-1$ . How many units apart are $A$ and $B$ ?
Answer: ______________

undefinedRatiosratios-grade6

1.
A recipe uses flour and sugar in the ratio $5:2$ . If you use $35$ cups of flour, how many cups of sugar do you need?
Answer: ______________
2.
Share $84 between two people in the ratio $2:5$ . How many dollars does the person with the larger share receive?
Answer: ______________
3.
Share $84$ marbles among three children in the ratio $2:3:7$ . How many marbles does the child with the smallest share get?
Answer: ______________
4.
In a bag, the ratio of red to blue marbles is $3:4$ . There are $28$ blue marbles. How many red marbles are there?
1. (A)
  $12$
2. (B)
  $21$
3. (C)
  $36$
4. (D)
  $84$
5.
In a class the ratio of boys to girls is $2:3$ . After $4$ more boys join, the ratio becomes $4:5$ . How many students are in the class now?
1. (A)
  $45$
2. (B)
  $50$
3. (C)
  $54$
4. (D)
  $60$

undefinedRate and speedrate-speed

1.
A car travels $180$ km in $2.5$ hours. What is its speed in km/h?
Answer: ______________
2.
Apples cost $7.50 for $5$ pounds. What is the price per pound, in dollars?
Answer: ______________
3.
Convert $20$ m/s to km/h.
Answer: ______________
4.
A cyclist rides at $60$ km/h for $1$ hour, then at $40$ km/h for $2$ hours. What is the average speed for the whole ride?
1. (A)
  $50$ km/h
2. (B)
  $46\tfrac{2}{3}$ km/h
3. (C)
  $48$ km/h
4. (D)
  $100$ km/h
5.
Jo walks $3$ km to school at $4$ km/h and takes the bus back along the same road at $12$ km/h. What is Jo's average speed for the round trip, in km/h?
Answer: ______________

undefinedPercent and percent changepercent-change

1.
Increase $80$ by $25\%$ .
Answer: ______________
2.
$15\%$ of what number is $36$ ?
Answer: ______________
3.
A price rose from $40 to $50. What was the percent increase?
Answer: ______________
4.
A jacket costs $45 after a $25\%$ discount. What was the original price?
1. (A)
  $33.75
2. (B)
  $56.25
3. (C)
  $60
4. (D)
  $70
5.
A number is decreased by $20\%$ , and the result is then increased by $20\%$ . The final value is what percent of the original? Enter the percent as a number.
Answer: ______________

undefinedArea of plane figuresarea-triangles-trapezoids

1.
A triangle has base $10$ cm and height $6$ cm. What is its area in cm²?
Answer: ______________
2.
A trapezoid has parallel sides of $8$ cm and $12$ cm and a height of $5$ cm. What is its area in cm²?
Answer: ______________
3.
A parallelogram has a base of $9$ cm. Its slanted side is $5$ cm long, and the perpendicular distance between the base and the opposite side is $4$ cm. What is its area?
1. (A)
  $18$ cm²
2. (B)
  $26$ cm²
3. (C)
  $36$ cm²
4. (D)
  $45$ cm²
4.
A triangle has area $24$ cm² and base $8$ cm. What is its height in cm?
Answer: ______________
5.
A parallelogram has base $12$ cm and height $7$ cm. A triangle with base $6$ cm and height $4$ cm is cut out of it. What is the area of the remaining shaded region, in cm²?
Answer: ______________

undefinedVolume and surface areavolume-surface-nets

1.
A box measures $3$ cm by $4$ cm by $5$ cm. What is its surface area in cm²?
Answer: ______________
2.
Find the volume of a rectangular prism with edges $2\dfrac{1}{2}$ cm, $1\dfrac{1}{3}$ cm, and $3$ cm, in cm³.
Answer: ______________
3.
A cube has a surface area of $150$ cm². What is the length of one edge, in cm?
Answer: ______________
4.
A box measures $2 \times 3 \times 6$ . When its net is drawn, which of these is not the area of one of the faces?
1. (A)
  $6$
2. (B)
  $9$
3. (C)
  $12$
4. (D)
  $18$
5.
A rectangular tank has volume $7\dfrac{1}{2}$ cubic feet. Its base is $2\dfrac{1}{2}$ ft by $2$ ft. How tall is it, in feet?
Answer: ______________

undefinedDisplaying and comparing datadata-distributions-6

1.
Which of these is a statistical question?
1. (A)
  How old am I?
2. (B)
  How tall is the principal?
3. (C)
  How many hours of sleep do sixth graders at our school get on a school night?
4. (D)
  What is $7 \times 8$ ?
2.
Find the median of $3,\ 7,\ 8,\ 12,\ 15,\ 20,\ 21$ .
Answer: ______________
3.
Find the interquartile range (IQR) of $3,\ 7,\ 8,\ 12,\ 15,\ 20,\ 21,\ 25$ .
Answer: ______________
4.
Five students' scores on a quiz were $2,\ 3,\ 3,\ 4,\ 40$ . Which is the better description of a typical score, and why?
1. (A)
  The mean, $10.4$ , because it uses every value
2. (B)
  The median, $3$ , because the $40$ pulls the mean far from where most scores are
3. (C)
  The range, $38$ , because it shows how different the scores are
4. (D)
  The mean, $10.4$ , because it is larger
5.
Find the mean absolute deviation (MAD) of $4,\ 8,\ 5,\ 7,\ 6$ .
Answer: ______________