Advanced Math 5 — every item

Singapore Dimensions Math 5A / 5B · 45 items

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

01Whole numbers to one billionplace-value-billion

1.
Round $438{,}516{,}207$ to the nearest million.
Answer: ______________
2.
A roll of ribbon is $3.45$ m long. A factory has $10^3$ rolls. What is the total length of ribbon, in metres?
Answer: ______________
3.
One bead has a mass of $4.2$ grams. What is the mass of $100$ beads, in grams?
1. (A)
  $4.200$
2. (B)
  $42$
3. (C)
  $420$
4. (D)
  $4{,}200$
5. (E)
  $0.042$

1.
Write $72$ as a product of primes in index notation. What is the exponent of $2$ ?
Answer: ______________
2.
Using $24 = 2^3 \cdot 3$ and $90 = 2 \cdot 3^2 \cdot 5$ , find $\text{LCM}(24, 90)$ .
Answer: ______________
3.
A red light flashes every $8$ seconds and a blue light flashes every $12$ seconds. They flash together now. In how many seconds will they next flash together?
1. (A)
  $4$
2. (B)
  $48$
3. (C)
  $96$
4. (D)
  $24$

1.
Compute $48 \times 25$ .
Answer: ______________
2.
A school orders $148$ boxes of pencils. Each box holds $25$ pencils. The school hands out one pencil to each of its $3{,}512$ students. How many pencils are left over?
Answer: ______________
3.
Which is the product $312 \times 204$ ?
1. (A)
  $63{,}648$
2. (B)
  $7{,}488$
3. (C)
  $62{,}400$
4. (D)
  $64{,}848$

1.
Compute $2{,}856 \div 34$ .
Answer: ______________
2.
A ribbon $1{,}574$ cm long is cut into $22$ equal pieces. How long is each piece, in cm? Give your answer as a mixed number in simplest form.
Answer: ______________
3.
A bakery packs $2{,}350$ cookies into boxes of $36$ . How many full boxes can it pack?
1. (A)
  $66$
2. (B)
  $65$
3. (C)
  $65\frac{5}{18}$
4. (D)
  $650$

1.
Four friends share $3$ pizzas equally. What fraction of a pizza does each friend get?
Answer: ______________
2.
A ribbon $4$ m long is cut into $5$ equal pieces. How long is each piece, in metres? Enter a decimal.
Answer: ______________
3.
Five friends share $2$ loaves of bread equally. How much bread does each friend get?
1. (A)
  $\frac{1}{5}$ of a loaf
2. (B)
  $\frac{2}{5}$ of a loaf
3. (C)
  $\frac{1}{2}$ of a loaf
4. (D)
  $2\frac{1}{2}$ loaves
5. (E)
  $10$ loaves

1.
Compute $3\dfrac{1}{4} - 1\dfrac{2}{3}$ . Give your answer as a fraction or mixed number.
Answer: ______________
2.
Mia has a ribbon $60$ cm long. She uses $\dfrac{1}{4}$ of it for a bow, then $\dfrac{2}{3}$ of the remainder for a bookmark. How many centimetres of ribbon are left?
Answer: ______________
3.
Jo had $40$ beads. She gave $\dfrac{2}{5}$ of them to Ali, then $\dfrac{1}{4}$ of the remainder to Bea. How many beads does Jo have left?
1. (A)
  $6$
2. (B)
  $14$
3. (C)
  $24$
4. (D)
  $18$

1.
Compute $\dfrac{3}{4} \times \dfrac{2}{5}$ .
Answer: ______________
2.
A ribbon $4$ m long is cut into pieces each $\dfrac{1}{5}$ m long. How many pieces are there?
Answer: ______________
3.
A garden plot is $\dfrac{2}{3}$ m wide and $\dfrac{4}{5}$ m long. What is its area, in m²?
1. (A)
  $\frac{3}{4}$
2. (B)
  $\frac{22}{15}$
3. (C)
  $\frac{8}{15}$
4. (D)
  $\frac{2}{5}$

1.
Five students scored $7$ , $12$ , $9$ , $15$ , and $12$ on a quiz. What is the mean score?
Answer: ______________
2.
The line plot below shows the lengths of $8$ ribbons.

Length (m) $\frac{1}{2}$ $\frac{3}{4}$ $1$
Number of ribbons $3$ $2$ $3$

What is the mean length, in metres?
Answer: ______________
3.
The line plot below shows how far $10$ paper airplanes flew.

Distance (m) $1$ $1\frac{1}{2}$ $2$ $2\frac{1}{2}$
Number of airplanes $2$ $3$ $4$ $1$

What is the mean distance, in metres?
1. (A)
  $2.5$
2. (B)
  $1.75$
3. (C)
  $1.7$
4. (D)
  $4.25$
5. (E)
  $17$

Length (m)	$\frac{1}{2}$	$\frac{3}{4}$	$1$
Number of ribbons	$3$	$2$	$3$

Distance (m)	$1$	$1\frac{1}{2}$	$2$	$2\frac{1}{2}$
Number of airplanes	$2$	$3$	$4$	$1$

1.
Two angles sit side by side on a straight line. One of them is $48^\circ$ . What is the other angle, in degrees?
Answer: ______________
2.
Two straight lines cross at point $P$ . One of the four angles at $P$ is $35^\circ$ . A third line cuts the two lines at $Q$ and $R$ , making triangle $PQR$ , and the triangle's angle at $P$ is vertically opposite the $35^\circ$ angle. The triangle's angle at $Q$ is $60^\circ$ . What is the triangle's angle at $R$ , in degrees?
Answer: ______________
3.
In triangle $ABC$ , $\angle A = 50^\circ$ and $\angle B = 60^\circ$ . Side $BC$ is extended past $C$ to a point $D$ . What is $\angle ACD$ ?
1. (A)
  $110^\circ$
2. (B)
  $70^\circ$
3. (C)
  $130^\circ$
4. (D)
  $100^\circ$

1.
On a coordinate grid, point $P$ is $4$ units to the right of the origin and $7$ units up. What is the $y$ -coordinate of $P$ ?
Answer: ______________
2.
Mia's mean score on four spelling tests is $82$ . Her first three scores were $80$ , $85$ , and $78$ . What was her fourth score?
Answer: ______________
3.
A bus travels $40$ km every hour. Ali graphs the trip with time in hours on the horizontal axis and distance in km on the vertical axis. Which point shows the bus after $3$ hours?
1. (A)
  $(120, 3)$
2. (B)
  $(3, 40)$
3. (C)
  $(3, 120)$
4. (D)
  $(40, 120)$

1.
Mia mixes red and white paint in the ratio $3:4$ . She uses $12$ cups of red paint. How many cups of white paint does she use?
Answer: ______________
2.
Ali and Bea have $30$ beads altogether, in the ratio $2:3$ . Ali gives Bea some beads, and now the ratio of Ali's beads to Bea's beads is $1:4$ . How many beads did Ali give to Bea?
Answer: ______________
3.
The red and blue beads on a necklace are in the ratio $3:5$ . The necklace has $40$ beads. How many are red?
1. (A)
  $5$
2. (B)
  $15$
3. (C)
  $24$
4. (D)
  $25$

1.
A bus travels $180$ km in $3$ hours. What is its speed, in km per hour?
Answer: ______________
2.
Ali can paint a fence in $4$ hours. Bea can paint the same fence in $12$ hours. Working together at these rates, how many hours do they take to paint the fence?
Answer: ______________
3.
A pump fills $\dfrac{3}{4}$ of a tank in $2$ hours. At this rate, how many hours does it take to fill the whole tank?
1. (A)
  $1\frac{1}{3}$
2. (B)
  $1\frac{1}{2}$
3. (C)
  $2\frac{2}{3}$
4. (D)
  $2\frac{3}{4}$

1.
Find $15\%$ of $60$ .
Answer: ______________
2.
A jacket is priced at $60. It is on sale for $25\%$ off, and then $6\%$ sales tax is added to the sale price. What is the final price, in dollars?
Answer: ______________
3.
A bus ticket costs $80. The price is increased by $5\%$ . What is the new price?
1. (A)
  $85
2. (B)
  $88
3. (C)
  $4
4. (D)
  $84