I have been teaching mathematics in an Australian High School since 1982, and I am a contributing author to mathematics text books.
Simple Maths Questions
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:
- “You should be asking your teacher. That’s their job.”
- “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.”
A Refresher Course
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.
Here is a range of 20 key questions (and their solutions) 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 work on these questions to highlight areas that you both competently attempted.
But don’t despair if your score is not as high as you expected. After all, these questions are supposed to be a fun and informative way of illustrating basic mathematics.
Read More From Wehavekids
Note: You may use a calculator to assist you.
When you finish solving the problems, go through the worked solutions provided.
This will really make you feel that you are back at school.
Worked solutions and discussion
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.
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
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.
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.
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.
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.
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.
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
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
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
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)
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)
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.
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.
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.
We can test each choice of answer to see which one is true.
1. add 5 and double.
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.
2. add 15.
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.
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.
This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.
© 2018 George Dimitriadis
Kari Poulsen from Ohio on January 05, 2018:
I enjoyed the test. Made me brush up on my knowledge, lol. I love math. Great hub!
K S Lane from Melbourne, Australia on January 04, 2018:
I'm not a parent, but I do help my sister with her maths homework when she's struggling and I'm a little ashamed that I couldn't answer some of these. I need to hit the books again if I'm going to be a better help to her. Thanks for the wake up call!
nicey on January 03, 2018:
Fantastic hub! If parents take time to look at their kids Maths homework, it's not that hard. They just need to conquer fear of maths. Thanks.