Grade 6 Math Practice Test
Grade 6 math practice test questions are presented along with their solutions .
1  Numbers

Which of the following properties
a) associativity b) commutativity c) distributivity d) identity of addition e) identity of multiplication
are used to write the following equalities ?

Which of the following numbers are prime numbers?
0,1,2,3,4,5,6,7,8,9,10,11

In which place value is the 2 in the number 1296 ?

Evaluate the expressions

Which digit is in the tenths place in the number 12.83 ?

Round to the nearest whole number.
a) 0.41 b) 1.2999 c) 123.5

Which of the following statements is true ?
a) 0.1 > 0.3 b) 1.2 < 1.3 c) 0.5 < 0.05

Evaluate the following expressions
a) 0.4 × 3 b) 8  3 × 0.2 c) 0.5 ÷ 5 \( \)\( \)\( \)2  Factors, Multiples and Divisibility of Numbers
 What is the Greatest Common Factor (GCF) of \( 8 \) and \( 12 \) ?
 What is the Least Common Multiple (LCM) of \( 3 \) and \( 7 \) ?
 Which of the following numbers is divisible by \( 5 \) ?
a) \( 125 \) b) \( 123 \) c) \( 200 \)
 Which of the following numbers is divisible by \( 2 \) ?
a) \( 35 \) b) \( 280 \) c) \( 476 \)

Which of the following numbers is divisible by \( 3 \) ?
a) \( 105 \) b) \( 101 \) c) \( 234 \)3  Fractions and Mixed Numbers
 Which of the following are improper fractions ?
a) \( \displaystyle \frac{2}{5} \) b) \( \displaystyle \frac{10}{3} \) c) \( \displaystyle \frac{3}{3} \)
 Convert the following improper fractions to mixed numbers.
a) \( \displaystyle \frac{7}{5} \) b) \( \displaystyle \frac{8}{3} \) c) \( \displaystyle \frac{9}{2} \)
 Find the missing numerator or denominator that makes each of the following pairs of fractions equivalent.
a) \( \displaystyle \frac{1}{2} = \frac{?}{4} \) b) \( \displaystyle \frac{2}{5} = \frac{6}{?} \) c) \( \displaystyle \frac{1}{3} = \frac{?}{9} \)
 Evaluate the following expressions (no need to reduce final answer).
a) \( \displaystyle \frac{4}{10}  \frac{1}{10}\) b) \( \displaystyle \frac{1}{2} + \frac{3}{4} \) c) \( \displaystyle \frac{1}{2} \times \frac{2}{3} \)
d) \( \displaystyle \frac{3}{4} \div \frac{1}{2} \) e) \( \displaystyle \frac{3}{4} \div 3 \) f) \( \displaystyle 2 \times \frac{2}{6} \)
g) \( \displaystyle 1\frac{1}{4} + 2\frac{1}{4} \) h) \( \displaystyle 3\frac{2}{5}  1 \frac{1}{5} \)
 Write as a decimal
a) \( \displaystyle \frac{7}{10} \) b) \( \displaystyle \frac{17}{100} \)

In the diagrams below a whole circle or square is one unit. Represent each of the colored (in red) parts as a fraction or a mixed number.
a)
b)
c)
4  Exponents
 Rewrite the following expressions using exponents.
a) \( 2 \times 2 \times 2 \times 2 \times 2 \) b) Five squared c) \(4\) cubed d) \(6\) to the seventh power

Evaluate the following expressions
a) \( 2^3 \) b) \( 1^5 \) c) \( 4^2 \) d) \( 1000^0 \)5  Ratios and Rates
 There are \( 2 \) red balls and \( 3 \) blue balls in a bag. What is the ratio of
a) red to blue balls ? b) blues to red balls ? c) blue to the total number of balls ?
 There are \( 11 \) girls and \( 8 \) boys in a class. What is the ratio of
a) girls to boys ? b) boys to the total number of students ?

Sam bought \( 5 \) kilograms of tomatoes at the cost of \( \$15 \). Find the unit rate (or price) in dollars / kilogram.
 A car traveled \( 120 \) kilometers (km) in \( 2 \) hours (hrs). Find the unit rate in km / hr.

There are \( 600 \) students in a school and the ratio of boys to girls is equal to \( 1:3 \). How many boys are in this school ?
6  Percent and Related Problems
 What is \( 60\% \) of \( 20 \)?
 Write \( 35\% \) as a decimal number.
 Write \( 15\% \) as a reduced fraction.
 What is \( 50\% \) of \( \displaystyle \frac{1}{4} \)?
 Write the fraction \( \displaystyle \frac {3}{5} \) as a prcentage.
 Amanda has a monthly salary of \( $3000 \). She spends \( $600 \) per month on clothes. What percent of her monthly salary does Amanda spend on clothes ?
 The price of an item changed from \( $125 \) to \( $100 \). What was the change in percent ?

A shirt initially costs \( \$40 \) and its has been discounted by \( 40\% \). What is the price of the shirt after the discount ?
7  Convert Units of Measurement

How many hectoliters \( (\text{ hL}) \) are in \( 320 \) liters \( (\text{ L}) \) knowing that \( 1 \text{ hl} = 100 \text{ L} \)?
 How many meters \( (\text{ m}) \) are in \( 234500 \) millimeters \( (\text{ mm}) \) knowing that \( 1 \text{ m} = 1000 \text{ mm} \)?
 How many kilometers \( (\text{ km}) \) are in \( 2300 \) meters \( (\text{m}) \) knowing that \( 1 \text{ km} = 1000 \text{ m} \)?
 How many milliliters \( (\text{ mL}) \) are in \( 1.2 \) liters \( (\text{ L}) \) knowing that \( 1 \text{ L} = 1000 \text{ mL} \) ?
 How many hours \( (\text{hrs}) \) are in \( 7200 \) seconds \( (\text{ sec}) \) knowing that \( 1 \; \text{ hr} = 3600 \; \text{ sec} \) ?
 How many many miles \( (\text{ mi}) \) are in \( 2640 \) yards \( (\text{yd}) \) knowing that \( 1 \text{ mi} = 1760 \text{ yd} \)?

How many many inches \( (\text{in}) \) are in \( 3 \) meters \( (\text{m}) \) knowing that \( 1 \text{ m} = 39.37 \text{ in} \)?
8  Mathematical Expressions
 Evaluate the expression \( \; x + 2 \; \) for \( x = 0.2 \)
 Evaluate the expression \( \; 2 (x + 2) \; \) for \( x = 3 \)
 Evaluate the expression \( \; a  b \; \) for \( a = 3 \) and \( b = 2 \)

Evaluate the expression \( \; \displaystyle \frac{2 x}{3} \; \) for \( x = 6 \)

Write mathematical expressions and equations for
a) \( 3 \) less than \( x \) b) \( 5 \) times \( (x+2) \) c) \( (2x +1) \) squared d) The sum of \( x \) and \( 1 \) multiplied by \( 3 \) is equal to \( 2 \). 
Write mathematical inequalities for
a) \( 3 \) is less than \( x \) b) \( 5 \) is at least \( x \) c) \( y \) is at most \( 9 \) d) The difference of \( x \) and \( 2 \) is less than or equal to \(  2 \). 
Expand the brackets and simplify.
a) \( 2(x + 4) \) b) \( 3 (a + b +2) \) c) \( \displaystyle \frac{1}{4}( 8 x + 4) \) d) \( 0.2 (x + 2) \) 
Factor the expressions
a) Find the Greatest Common Factor (GCF) of \( 9 \) and \( 6 \)
b) Write \( 9 \) and \( 6 \) as a product of the GCF found in a) and another number.
c) Write \( 9 x + 6 \) as the product of the GCF found in a) and an expression between brackets.9  Equation with One Variable and Related Problems
 Solve the equations
a) \( x + 2 = 8\) b) \( 2 x = 6 \)
c) \( x  3 = 7 \)

The perimeter of a rectangular garden is \( 10 \) meters and its length is \( 3 \) meters. Let \( x \) be the width of the garden.
a) Write an equation in \( x \) to solve for the width.
b) Solve the equation obtained in part a)
c) Check your answer to the problem.10  Coordinate Plane
 Identify the quadrant or axis on a coordinate plane of each point without plotting them.
a) \( (0,1) \) b) \( (2,3) \) c) \( (2,9) \)
d) \( (4,6) \) e) \( (3,4) \) f) \( (3,0) \)

Determine the coordinates of the points on the coordinate plane below.

John is walking at a constant speed of 5 kilometers per hour (km/hr).
a) Complete the table below where \( d \) is the distance, in kilometers (km), walked and \( t \) is the time, in hours (hrs), taken to walk distance \( d \).
b) Plot the points on the coordinate plane and join the points obtained.
.11  Inequalities

Represent the numbers \( 4, 0 , 5 , 6 , 4 \) on a number line and decide which of the following statements is true.
a) \( 4 \lt 0 \) b) \( 0 \gt 4 \) c) \( 6 \lt 4 \)
d) \( 6 \gt 5 \) e) \( 0 \lt 6 \)12  Geometry
 Select the correct answer. The sum of all internal angles of a triangle is equal to
a) \( 360^{\circ} \). b) \( 180^{\circ} \). b) \( 270^{\circ} \).

Select the correct answer. Two straight lines intersect at point \( O \). In the figure below angles \( \angle AOB \) and \( \angle BOC \) are
a) Complementary. b) Supplementary. b) Neither Complementary nor supplementary.

Three straight lines intersect at point \( O \). Which these pairs of angles are vertical?
a) \( \angle AOB \; \text{and} \; \angle DOF \quad \) , b) \( \angle BOC \; \text{and} \; \angle EOF \quad \) , c) \( \angle COD \; \text{and} \; \angle FOB \)
d) \( \angle FOB \; \text{and} \; \angle COE \quad \) , e) \( \angle AOC \; \text{and} \; \angle DOE \quad \) , f) \( \angle BOD \; \text{and} \; \angle EOA \)
 Give the number of sides of each of the geometric figures listed below.
a) Pentagon b) Trapezoid c) Triangle c) Kite
 Which of the following is true about an isosceles triangle ?
a) Two of its angles are equal but the three sides are different.
b) Two angles are equal and the opposite sides to the equal angles are equal.
C) Two sides are equal but all the angles are different.
 Calculate the perimeter of a rectangle with a length of \( 10 \) cm and a width of \( 5 \) cm.
 Calculate the area of a circle of radius \( 1 \) m.

ABCD is a rectangle bounded on the left side by segment AE. Find the area of the shaded (in blue) surface given that the length of segment DE is equal to 2 cm. (Figure not to scales)
13  Three Dimensional Figures

Determine the number of edges and faces of the truncated pyramid shown below.

Given the rectangular prism below,
a) Find the area of the rectangles ABCD, ADHE and DCGH
b) Find the surface area of the rectangular prism.
c) Find the volume of the rectangular prism

Given that the volume of the triangular prism below is \( 24 \), find its total surface area.
14  Data and Graphs

The numbers of hours Harry spent training for his soccer match during 5 days of the week are shown in the line plot below.
How many hours did Harry spend training for his match during the week ?

The number of students (on the vertical axis) and the range of scores (on the horizontal axis) on an English test are shown in the histogram below.
a) How many students scored in the range 9099 ?
b) How many more students scored in the range 8089 than students who scored in the range 6069 ?
15  Statistics

Calculate the range, mean, mode and median of the data set: \( \{ 1 , 4 , 2 , 2 , 3 , 2 , 7 \} \)
16  Probabilities
 Which of the following cannot be a measure of probability ?
a) 1 b) 0.5 c) 2 d) 0 e) 0.0001
 a) How many outcomes are possible if you flip a coin ?
b) How many outcomes are possible if you select one of five different cards at random ?
c) How many outcomes are possible if you flip a coin and select one of five different cards at random ?

a) What are all the possible outcomes if you roll a fair die with numbers from 1 to 6 on the 6 faces ?
When you roll a fair die, with numbers from 1 to 6 on the faces, what is the probability that
b) the number obtained is equal to 0 ?
c) the number obtained is equal to 5 ?
c) the number obtained is greater than 4 ?
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