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# Simple Mathematics Questions That Every Parent Should Know

I have been teaching mathematics in an Australian High School since 1982, and I am a contributing author to mathematics text books.

You are a concerned parent of school-aged children but often feel helpless during turbulent moments, such as when they are completing mathematics homework.

“Mummy, I can’t do my mathematics homework. Can you help me, please?”

And you lie, “I’m very busy right now, dear. Can you ask your father?”

“Dad, Mummy’s busy. Can you help me do my mathematics homework?”

Your husband is a better liar than you. “Sorry, son. I’m just about to make an important phone call.”

Occasionally, utterly frustrated by your mathematical impotence, pleas for assistance elicit caustic retorts which you immediately regret making, such as

• “Didn’t you pay attention in class when the teacher explained it.”
• “I’m your mother, not a mathematics genius. Keep trying to work it out.”
• “If you spent more time doing homework instead of watching TV and using the internet, you’d know what to do.”

Bitter replies may be valid to some degree, but they do not ameliorate the situation.

Your mathematics knowledge was sufficient to carry you and your children through their formative primary school years, but you now struggle to come to terms with algebra, geometry and square roots.

Take the following quiz. It consists of a range of 20 key questions that reflect the required knowledge in some important topics in mathematics typically taught to junior-level high school students.

Comments on each solution will provide you with a snapshot of your overall understanding.

It may also be a good idea for your child to take the quiz to highlight questions that you both competently attempted.

But don’t despair if your score is not as high as you expected. Attempt the quiz with its intended purpose, to be a fun and informative way of illustrating basic mathematics.

Note: You may use a calculator to assist you.

When you finish the quiz, go through the worked solutions provided.

This will really make you feel that you are back at school.

## Quiz

For each question, choose the best answer. The answer key is below.

1. How many digits are in the number 200.00?
• 5
• 1
• 2
• 6
2. When we fully simplify the fraction 8/20 we get
• 4/10
• 2/5
• 4/20
• 1/10
3. The area of a square of side length 8 metres is
• 16 square metres
• 24 square metres
• 48 square metres
• 64 square metres
4. What is the perimeter of a rectangle of length 6 cm and width 5 cm?
• 30 cm
• 22 cm
• 11 cm
• 17 cm
5. Two interior angles of a triangle are 30 degrees and 40 degrees. The third angle must be
• 70 degrees
• 120 degrees
• 110 degrees
• 10 degrees
6. An angle of 105 degrees is described as being what type of angle?
• obtuse
• reflex
• acute
• straight
7. The volume of a ‘box” of length 2 metres, width 5 metres and height 4 metres is
• 20 cubic metres
• 10 cubic metres
• 11 cubic metres
• 40 cubic metres
8. The circumference of a circle with diameter 200 centimetres is
• 314 square centimetres
• 400 square centimetres
• 100 square centimetres
• 628 square centimetres
9. The area of a semicircle with radius 10 metres is closest to
• 314 metres
• 50 metres
• 157 metres
• 107 metres
10. The number 24 divided in the ratio 1 : 3 gives
• 10 and 14
• 12 and 12
• 8 and 16
• 6 and 18
11. What is the cube root of 64?
• 2
• 10
• 4
• 8
12. The price of a \$500 TV is reduced by 15%. How much do you pay?
• \$450
• \$405
• \$425
• \$410
13. If a = 2, b = 4 and c = 5, then 3ab – 4c is
• 6
• 2
• 8
• 4
14. Expanding 4(3c + 7d – 2) gives
• 7c + 11d + 2
• 12c + 28d - 8
• 43c + 47d - 42
• 4372cd
15. Factorising 15e – 10g gives
• (15 - 10)(e - g)
• 15(e - g)
• 5(3e - 2g)
• 150eg
16. The solution for x in the equation 2x + 5 = 21 is
• 8
• 6
• 4
• 2
17. If x = 7, which is true?
• 3x < 20
• 2x - 1 > 10
• 8x + 3 = 60
• 5x - 34 = 0
18. The number of vertices, edges and faces of a cube is, respectively
• 6, 8, 12
• 12, 8, 6
• 6, 12, 8
• 8, 12, 6
19. Which statement is true concerning adding two fractions together?
• The denominators are added together
• Both fractions must have the same denominator
• The numerators are multiplied together
• Both fractions must have the same numerator
20. What is the rule for finding the next number in the sequence 20, 35, 65, …?
• triple and then subtract 25
• double and then subtract 5

1. 5
2. 2/5
3. 64 square metres
4. 22 cm
5. 110 degrees
6. obtuse
7. 40 cubic metres
8. 628 square centimetres
9. 157 metres
10. 6 and 18
11. 4
12. \$425
13. 4
14. 12c + 28d - 8
15. 5(3e - 2g)
16. 8
17. 2x - 1 > 10
18. 8, 12, 6
19. Both fractions must have the same denominator
20. double and then subtract 5

If you got between 0 and 6 correct answers: It might be beneficial to all parties if you let your child show YOU how to do the homework. This will provide you with some knowledge and skills, and your child will become motivated to do better.

If you got between 7 and 12 correct answers: If your score is at least 50%, you have demonstrated some understanding of basic mathematics. If you scored less than 50%, it might be a good idea to let your spouse help with the homework.

If you got between 13 and 16 correct answers: Not a bad score. You have a reasonable appreciation of the basic ideas and can be of some use to your children when they are completing their homework.

If you got between 17 and 18 correct answers: Well done! Your score indicates a solid mastery of the basics. You are probably already a good mathematics mentor to your child. Keep up the good work.

If you got between 19 and 20 correct answers: You are either a mathematics teacher or someone that has studied mathematics at university. You obviously have no problems with helping your child with homework, at least until they go to university.

Worked solutions and discussion

Question 1

A digit is one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

So, for example, there are 4 digits in the number 6078.

For 200.00, there are 5 digits. We do not count the decimal point.

Question 2

To simplify a fraction, we divide the numerator (the top number) and the denominator (the bottom number) by the largest whole number that leaves no remainder.

For 8/20, the biggest number that divides both 8 and 20 is 4.

Now divide 8 and 20 by 4 to obtain the fraction 2/5

Question 3

To find the area of a square, we multiply its length by its width. Since the length is the same as the width, we work out length x length.

For this question, the length is 8 metres, so the area is 8 x 8 = 64 square metres.

Question 4

The perimeter of any side that has straight sides is found by adding the lengths of all of its sides. Our rectangle has lengths 6 cm, 5 cm, 6 cm, 5 cm.

The sum of these four numbers is 22, so the perimeter is 22 cm.

Question 5

The three interior angles of a triangle always sum to 180 degrees.

The first two angles are 30 degrees and 40 degrees, which sum to 70 degrees.

So we need to work out what number added to 70 makes 180. It must be 110.

So the third angle in the triangle is 110 degrees.

Question 6

Angles are named according to their size.

An angle of 105 degrees is between 90 degrees and 180 degrees, so it is called an obtuse angle.

Question 7

Question 8

Question 9

Question 10

The cube root of a number is another number that is multiplied with itself three times to give you the number.

If we want the cube root of 64, we find a number, say, N, so that N x N x N = 64.

In this case the number that works is 4, because 4 x 4 x 4 = 64.

Question 11

We first work out 15% of \$500.

This is the same as 15% x 500, or 0.15 x 500 or (15/100) x 500.

This gives \$75 as the discount.

So you pay \$500 - \$75 = \$425

Question 12

We substitute (replace) each letter with its assigned value.

Between two letters or between a number and a letter we always use multiplication.

So 3ab – 4c means 3 x 2 x 4 – 4 x 5 which is 24 – 20 = 4

Question 13

To expand means to multiply everything inside the brackets by what is in front of the brackets.

In this case we multiply 3c + 7d – 2 by 4

We write 4 x 3c + 4 x 7d + 4 x -2

This simplifies to 12c + 28d – 8

Question 14

To factorise means to insert brackets. What will go in front of the brackets is the biggest number that divides into 15 and into 10 at the same time. This number is 5.

So we have up to this stage something that looks like 5( )

To work out what is inside the brackets, we divide the 15e by 5, which is 3. We also divide 10g by 5, which is 2g.

Hence, 15e – 10g becomes 5(3e – 2g)

Question 15

2x + 5 = 21 means to find a number for x so that when we double it and add 5 to the result, the answer is 21.

You can try different values until you find a number that works. This is called the ‘trial and error’ method. The number that works is 8, because 2 x 8 + 5 =21

To work out the answer using algebra, we perform opposite operations to both sides of the = until we have the letter on its own. Here are the steps to follow.

2x + 5 = 21

2x + 5 – 5 = 21 – 5, (subtract 5 from both sides)

2x = 16 (simplify)

2x/2 = 16/2 (divide both sides by 2)

x = 8 (simplify)

Question 16

The symbol < means “less than” and > mean “greater than”.

We test to see if each choice of answer is true.

1. 3x < 20

If we use x = 7, 3x is 3 x 7 which is 21. This answer is not less than 20, so option 1 is False.

2. 2x – 1 > 10

If we use x = 7, 2x – 1 is 2 x 7 – 1 which is 13. This value is greater than 13, so option 2 is True.

3. 8x + 3 = 60

Using x = 7, 8x + 3 is 8 x 7 + 3 which is 59. This answer is not 60, so option 3 is False.

4. 5x – 34 = 0.

With x = 7, 5x – 34 is 5 x 7 – 34 which is 1. We require this to be o, so option 4 is False.

The only correct answer is option 2.

Question 17

For a 3-dimensional shape:

an edge is a straight line

a vertex (plural is vertices) is where two or more edges meet.

a face is a flat area.

A cube has 8 vertices, 12 edges and 6 faces.

Each face is in the shape of a rectangle.

Question 18

To add two fractions together, the denominators of both fractions must first be the same.

When they are the same, we obtain the answer by adding the numerators.

Question 19

We can test each choice of answer to see which one is true.

This means we add 5 to each number and double the result to get the next number. If we do this to 20, we get (20 + 5) x 2 which is 50. But the next number is 35, so option 1 is False.

This is clearly False because 35 + 15 is 50, not 65.

3. triple and subtract 25.

Using 20, we have 20 x 3 – 25 which is 35.

Using 35 we obtain 35 x 3 – 25 which is 80. But we should get 65, so option 3 is False

4. double and subtract 5.

Using 20, we obtain 20 x 2 – 5 which is 35.

Using 35 we have 35 x 2 – 5 which gives 65. So option 4 is True.

Question 20

A ratio of 1:3 means there the number is divided into 2 numbers and there are 1 + 3 = 4 parts altogether.

The first number has 1 part (1/4) and the second number has 3 parts (3/4).

The first number is ¼ of 24 which is 6.

The second number is ¾ of 24, which is 18.