Page 128 - Maths Skills - 7

126 Maths

Example 3: Find the value of the following expressions for p = 2, q = – 3 and r = – 1.

(i) 2p – 7q + 5r – 5 (ii) 3pq – 4p q + 18pqr
2
2
Solution: (i) 2p – 7q + 5r – 5 for p = 2, q = – 3, r = – 1
= 2 × 2 – 7 × (– 3) + 5 × (– 1) – 5

= 4 + 21 – 5 – 5 = 25 – 10 = 15
(ii) 3pq – 4p q + 18pqr for p = 2, q = – 3 and r = –1
2
2
= 3 × 2 × (– 3) – 4 × 2 × (– 3) + 18 × 2 × (– 3) × (– 1)
2
2
= 54 + 48 + 108 = 210
y
Example 4: Evaluate: 2 + x + 4 + z + y for x = 7, y = – 2, z = 4.
y
Solution: 2 + x + 4 + z + y
−2
= + 7 + 4 + 4 + (– 2) = – 1 + 15 – 2 = 15 – 3 = 12.
2
bc
Example 5: Find the value of c × – (7 – a) for a = 4, b = 8 and c = 5.
4
bc 8 × 5
2
Solution: c × – (7 – a) = 5 × – (7 – 4) = 50 – 3 = 47
4 4

Exercise 7.3

1. Find the value of the following expressions using x = – 3:
7x 2
(i) x – 5 (ii) 9 – 3x (iii) 6x – 2x + 5 (iv) 2 – 5
2
3
2. If x = – 1 and y = – 2, find the value of:
(i) x y – 7 (ii) x + y – 2xy (iii) 60x + 7y (iv) – x – 3y + 2xy + 11
2
2
2
2
2
3. Simplify and find the value of the following expressions for t = – 4 and r = 2
(i) – 2t + 4r + 5t – 6r (ii) –3(t + r) + 4 (2t – 3r) – (2t – r)
2
4. Simplify the following expressions and find their values if a = 1, b = 2 and c = – 1.
(i) 3a + b + c – 4ab – a + 3ab – 5ac + 4ab – bc (ii) 6a c – 4b c – 3c a – bc – c – 2b c – a c
2
2
2
2
2
2
2
2
2
2
5. If p = – 25, then find the value of p – 3p + 2p + 5.
3
2
7 3
3
4
6. If g = – 7, find the value of g − g + 9g .
3 2
7. If x – xy + y = 15, and x = 2, find the value of y.
2
8. What should be the value of x if the value of 3y + 5y – x is – 2 for y = – 2 ?
2
9. Find the value of b if the value of 9a – 3b + 6ab is – 3 when a = – 2.
2
x + 3 y + 3 z 3
10. If x = – 2, y = – 3 and z = 1, find the value of: ·
3