Integers & Number Theory
(MCQ):
What is the result of −5+8?
A) 13
B) -3
C) 3
D) -13
C) 3
When adding a negative and a positive number, you subtract the smaller from the larger and keep the sign of the larger number. In this case, 8−5=3.
(Fill in the Blanks):
The fraction 10/25 in its simplest form is ______.
2/5
To simplify a fraction, you divide both the numerator and the denominator by their highest common factor, which in this case is 5. 10÷5=2 and 25÷5=5.
(True or False):
The expression 5x+2 is an equation.
False
An expression is a mathematical phrase that can contain numbers, variables, and operations but does not have an equal sign. An equation has an equal sign.
(MCQ):
How many millimetres are in 1 centimetre?
A) 1000
B) 100
C) 10
D) 1
C) 10
The metric system is based on powers of 10. There are 10 millimetres in 1 centimetre.
(MCQ):
An angle that measures exactly 90° is called a _______ angle.
A) Obtuse
B) Acute
C) Straight
D) Right
D) Right
By definition, an angle that is exactly 90 degrees is a right angle.
(True or False):
The Highest Common Factor (H.C.F.) of 8 and 12 is 4.
True
The factors of 8 are 1, 2, 4, 8. The factors of 12 are 1, 2, 3, 4, 6, 12. The highest number that appears in both lists is 4.
(True or False):
1/2 + 1/4 = 2/6.
False
To add fractions, you need a common denominator. 1/2 is equivalent to 2/4. So, 2/4 +1/4 = 3/4, not 2/6.
(MCQ):
If a=5 and b=3, what is the value of 2a−b?
A) 7
B) 13
C) -1
D) 2
A). 7
Substitute the values for a and b into the expression: 2(5)−3=10−3=7.
The area of a shape is the distance around its outer edge.
False
The area is the amount of surface a shape covers. The perimeter is the distance around its outer edge.
(Fill in the Blanks):
A triangle with all three sides of different lengths is called a _______ triangle.
scalene
A scalene triangle has no sides of equal length.
MCQ
What is the Lowest Common Multiple (L.C.M.) of 6 and 9?
A) 3
B) 18
C) 54
D) 36
B) 18
The multiples of 6 are 6, 12, 18, 24... The multiples of 9 are 9, 18, 27... The smallest multiple they have in common is 18.
(MCQ):
What is the decimal equivalent of 3/5?
A) 0.35
B) 0.6
C) 3.5
D) 0.5
B) 0.6
To convert a fraction to a decimal, divide the numerator by the denominator. 3÷5=0.6.
(Fill in the Blanks):
The solution to the equation x+7=12 is x=______.
5
To solve for x, you subtract 7 from both sides of the equation. 12−7=5
The perimeter of a rectangle with a length of 10 m and a width of 5 m is ______ m.
30
The perimeter of a rectangle is 2×(length+width). 2×(10+5)=2×15=30 m.
(True or False):
Two lines that never intersect are called parallel lines.
True
Parallel lines are lines in a plane that are always the same distance apart and never intersect.
(MCQ):
Which of the following is an integer?
A) 1/2
B) 3.5
C) -10
D) Square root of 2
C) -10
An integer is a whole number, including negative numbers and zero. Fractions and decimals are not integers.
(MCQ):
What is the value of 0.8×0.2?
A) 1.6
B) 0.16
C) 16
D) 0.016
B) 0.16
Multiply the numbers as if they were whole numbers: 8×2=16. Then, count the total number of decimal places in the original numbers (one in 0.8 and one in 0.2, for a total of two). Place the decimal point two places from the right in the answer, giving 0.16.
(MCQ):
Simplify the expression 3x+2y+4x−y.
A) 7x+3y
B) 7x+y
C) 7x−y
D) 6xy
B) 7x+y
To simplify, you combine like terms. 3x+4x=7x. 2y−y=y. The simplified expression is 7x+y.
MCQ
What is the area of a square with a side length of 6 cm?
A) 12 cm²
B) 24 cm²
C) 36 cm²
D) 48 cm²
C) 36 cm²
The area of a square is the side length multiplied by itself. 6×6=36 cm².
(Fill in the Blanks):
The sum of the interior angles in a triangle is ______ degrees.
180
The sum of the interior angles of any triangle is always 180 degrees.
MCQ (Fill in the Blanks):
The number of prime numbers between 20 and 30 is _____.
A. 2
B. 1
C. 3
D. 4
A. 2
The prime numbers between 20 and 30 are 23 and 29. A prime number has only two factors: 1 and itself.
(Fill in the Blanks):
The mixed number 2 1/2 is equivalent to the improper fraction ______.
5/2
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. The denominator stays the same. (2×2)+1=5, so the improper fraction is 5/2.
True or False:
x2+x2=x4.
False
When adding like terms, you add the coefficients but the variable and its power remain the same. x2+x2=2x2. You would get x4 if you were multiplying: x2 × x2=x2+2=x4.
True or False: 5 kilograms is equal to 500 grams.
False
There are 1000 grams in 1 kilogram. Therefore, 5 kilograms is 5×1000=5000 grams.
(Fill in the Blanks):
A _______ is a straight line that connects two points on the circumference of a circle and passes through the center.
diameter
The diameter is a straight line that connects two points on a circle, passing through the center. The diameter is twice the length of the radius.