HS Math Entrance Exam

Winifred saved $3 665.00 from his daily allowance. He spent $ 230.00 to buy a pair of shorts and $250.00 to buy a shirt. How much of his money was left?

A. $3 185

B. $5 381

C. $8 531

D. $1 853

E. $5 813

A small red box contains two marbles and a small blue box contains 1 marble. Lisa gets ten red boxes and one blue box of marbles respectively. How many marbles did Lisa get in all?

A. 18 marbles

B. 19 marbles

C. 20 marbles

D. 21 marbles

E. 22 marbles

Find the following angles asked from the figures below.

The angle ∠AGL measures 90°. If ∠AGN and ∠EGL are equal, find ∠NGE.

A. 55°

B. 60°

C. 65°

D. 70°

E. 75°

Find the measurement of ∠PAM.

A. 110.2°

B. 152.9°

C. 143.4°

D. 113.4°

E. 127.5°

From the figure, find the measure of ∠MAR.

A. 52.5°

B. 62.1°

C. 35.9°

D. 57.3°

E. 49.2°

Laura had 15 red ponytails which are her favorite. The red ponytail is 15% of all the ponytail Laura had. How many ponytails does Laura have altogether?

A. 70

B. 80

C. 90

D. 100

E. 110

Jim recorded his monthly savings deposit in the bank. He started at $5 000.00 in January 2022. In the succeeding months, he consistently adds 25% of his monthly standing balance into his savings account. How much will be his total savings in April 2022? Round your answer to two decimal places.

A. $9 671.76

B. $9 667.51

C. $9 765.63

D. $9 567.99

E. $9 551.75

Mia baked 2 whole homemade pineapple pies. She shared  ½  slice with her friend and another ¾  slice with her family. What is the remaining slice of pineapple pie left for her? 

A. ¼ 

B. ½ 

C. ¾ 

D. ⅓ 

E. ⅔ 

In the late afternoon, the shadow of a tower is exceedingly long due to the low position of the Sun. The tower is 20-m high and it casts a 99-m shadow. What is the distance from the top of the tower to the tip of its shadow?

A. 89 meters

B. 101 meters

C. 112 meters

D. 127 meters

E. 131 meters

To rescue a dog from a burning house, a 10-meter ladder is leaning on a wall and is positioned such that the base of the ladder is 6 meters away from the building. How far above the ground is the location of the dog that needs rescuing?

A. 7 meters

B. 8 meters

C. 9 meters

D. 10 meters

E. 11 meters

Write as one fraction and simplify

In a full set of permanent teeth, 1/x of the teeth are incisors, 1/x are premolars, and 3/2x are molars.  What fraction of all the teeth are incisors, premolars and molars?

A. 3/7x

B. 2/7x

C. 7/2x

D. 7/3x

E. 7/4x

 In a triangle, the ratio of the measures of three sides is 4 : 6 : 9, and it’s perimeter is 190 cm. Find the measure of each side.

A. 36 cm, 54 cm, 81 cm

B. 45 cm, 54 cm, 91 cm

C. 40 cm, 60 cm, 90 cm

D. 30 cm, 70 cm, 90 cm

E. 44 cm, 60 cm, 86 cm

A bus travels from Sydney to Melbourne in 512th of a day. The distance between the two cities is 877.7 kilometers. How fast was the bus going on average?

A. 87.77 kph

B. 85.77 kph

C. 83.77 kph

D. 81.77 kph

E. 79.77 kph

If x=4, find the following equations if they are true or false.

5 + 2x = 4x – 1

A. True 

B. False. 5 + 2x is greater than 4x – 1.

C. False. 5 + 2x is less than 4x – 1.

D. None of the above

If x=4, find the following equations if they are true or false.

9x – 7 = 3x + 17

A. True

B. False. 9x – 7 is greater than 3x + 17

C. False. 9x – 7 is less than 3x + 17

D. None of the above.

Daisy is a student assistant in the Mathematics department. Since she is hardworking and very pleasant to all, the department head decides to give her an additional $ 50 every week on top of the x per hour rate.

If she works for 4 hours a day, how much does she receive in 1 a week with 5 working days?

A. $ 28x+30

B. $ 26x+35

C. $ 24x+40

D. $ 22x+45

E. $ 20x+50

Daisy is a student assistant in the Mathematics department. Since she is hardworking and very pleasant to all, the department head decides to give her an additional $ 50 every week on top of the x per hour rate.

Write an expression that gives how much she should receive in two weeks. 

A. $ 15x+100

B. $ 20x+100

C. $ 30x+100

D. $ 40x+100

E. $ 50x+150

Find the mean, median, and mode of the following set of numbers.

{4, 3, 5, 7, 4, 9, 2, 4, 9}

A. Mean: 3.12, Median: 4, Mode: 4 

B. Mean: 6.52, Median: 5, Mode: 4

C. Mean: 4.78, Median: 3, Mode: 3

D. Mean: 6.34, Median: 5, Mode: 4

E. Mean: 5.22, Median: 4, Mode: 4

Roger and Mason are playing two dice that must be rolled. The first to have a doublet (equal numbers on both dice) wins. Find the probability of getting a doublet.

A. ⅙

B. ⅓

C. ½

D. ⅔

E. ⅚ 

 Based on the table below and the equations given, find the values of y with the given values of x.

y = 2x – 5

A. -14, -12, -10, -8, -6, -4, -2

B. -12, -10, -8, -6, -4, -2, 0

C. -11, -9, -7, -5, -3, -1, 1

D. -13, -11, -9, -7, -5, -3, -1

E. -9, -7, -5, -3, -1, 1, 3

Which line passes through the points (−1,0) and (0,−2)?

A. y =2x+2 

B. y =2x−2 

C. y =−2x+2 

D. y =−2x−2

E. y =−3x−2

A figure is shown below. Assume that lines AB and AD are parallel, and the measures of angles ∠ACB and ∠CDE are 90° and 30° respectively. Find the measure of angle ∠BAC.

A. 60°

B. 50°

C. 40°

D. 30°

E. 20°

A trapezium is a quadrilateral with no parallel sides.

The mean of a set of numbers is also called the average.

The Pythagora’s Theorem states that the area of the square whose side is the hypotenuse is equal to the difference of the areas of the squares on the other two sides.

The volume rule V=Ah can also be applied to prisms that have different shapes and bases.

Danny’s first planter is 244 cm long and 61 cm wide. The container is filled with soil to a height of 91 cm in the planter. What is the volume of soil in the planter in cubic meters?

The figure is formed by five rectangles.  Find the area of the unshaded region.

Belinda puts ½ of her weekly allowance in savings and uses ⅔ of the remaining money for food. If she has $100 left at the end of the week, how much did she have at first?