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Integers Questions
1. The sum of two numbers exceeds their product by one. Their difference is equal to their product less five. Find the two numbers. (3mks)
2. 3x – 1 > -4
2x + 1≤ 7
3. Find the value of x
2(x-3) x 8(x+2) = 128
4. Evaluate -12 ÷ (-3) x 4 – (-15)
-5 x 6 ÷ 2 + (-5)
5. Without using a calculator/mathematical tables, evaluate leaving your answer as a simple
fraction
(-4)(-2) + (-12) (+3) + -20 +(+4) + -6)
-9 –(15) 46- (8+2)-3
6. Given that P = and R = and if Z = P-1R. Find Z
7. Evaluate -8 2 + 12 x 9 – 4 x 6
56 7 x 2
Integers Answers
1. | Let the number be x and y x + y = xy – 1 y – x = xy – 5 x + y + 1 = xy y – x + 5 + = xy x + y + 1 = y – x + 5 2x = 4 x = 2 Y – 2 + 5 = 2y = y = 3 |
B1
B1
B1 | |
03 |
2. X > -1
X ≥ 3
3. 2x 23 x 8 xx 82 = 128
2x 23 x 23x x 82 = 128
Let 2x be y
y/8 x y3 x 64 = 128
8y/8 = 128/8
y4 = 16 M1
y4 = 24 M1
y = 2 A1
-5 x 6 ÷ 2 + (-5)
4. -12 -3 = 4
4 x 4 + 15
Numerator 16 + 15 = 31
Denominator -5 x 3 + -5 = 31
-15 + -5
-15 + -5
= -20
31
-20
= – 1 11/20
5. = (-8) – (-4) + (-16) + (-6)
-9 + 15 46 -13
= -12 + -22
6 33
= -2 – 2
3
= -2 2
3
6.
P-1 =
–1
5
P-1 R = =
=
7. -8 2 + 12 x 9 – 4 x 6
56 7 x 2
= -4 + 108 – 24
16
80
- = 5
