Exam Questions — Algebra
Filter by category and choose how many to show per page.
Showing 10 questions.
6 marks
Foundation
Edexcel
Algebra
\[ K = 8r + 4s \]
- a) (i) \[\text{Work out the value of } K \text{ when } r=2,\; s=6.\] (2 marks)
- a) (ii) \[\text{Work out the value of } r \text{ when } K=28,\; s=3.\] (2 marks)
- b) \[\text{Work out the value of } K \text{ when } r=-1,\; s=2.\] (2 marks)
a) (i)
Answer:
\[ K=8(2)+4(6)=16+24=40.\]
Solution:
\[8(2)+4(6)=40.\]
a) (ii)
Answer:
\[ 28=8r+4(3)=8r+12 \implies 8r=16 \implies r=2.\]
Solution:
\[28=8r+12 \implies r=2.\]
b)
Answer:
\[ K=8(-1)+4(2)=-8+8=0.\]
Solution:
\[8(-1)+4(2)=0.\]
6 marks
Foundation
Edexcel
Algebra
\[ G = 4m - n \]
- a) (i) \[\text{Work out the value of } G \text{ when } m=7,\; n=3.\] (2 marks)
- a) (ii) \[\text{Work out the value of } m \text{ when } G=15,\; n=5.\] (2 marks)
- b) \[\text{Work out the value of } G \text{ when } m=-2,\; n=4.\] (2 marks)
a) (i)
Answer:
\[ G=4(7)-3=28-3=25.\]
Solution:
\[4(7)-3=25.\]
a) (ii)
Answer:
\[ 15=4m-5 \implies 4m=20 \implies m=5.\]
Solution:
\[15=4m-5 \implies 4m=20 \implies m=5.\]
b)
Answer:
\[ G=4(-2)-4=-8-4=-12.\]
Solution:
\[4(-2)-4=-12.\]
6 marks
Foundation
Edexcel
Algebra
\[ F = 2x + 5y \]
- a) (i) \[\text{Work out the value of } F \text{ when } x=3,\; y=4.\] (2 marks)
- a) (ii) \[\text{Work out the value of } x \text{ when } F=21,\; y=2.\] (2 marks)
- b) \[\text{Work out the value of } F \text{ when } x=-2,\; y=6.\] (2 marks)
a) (i)
Answer:
\[ F=2(3)+5(4)=6+20=26.\]
Solution:
\[2(3)+5(4)=6+20=26.\]
a) (ii)
Answer:
\[ 21=2x+5(2)=2x+10 \implies 2x=11 \implies x=\tfrac{11}{2}.\]
Solution:
\[21=2x+10 \implies 2x=11 \implies x=11/2.\]
b)
Answer:
\[ F=2(-2)+5(6)=-4+30=26.\]
Solution:
\[2(-2)+5(6)=-4+30=26.\]
6 marks
Foundation
Edexcel
Algebra
\[ H = 6p + 3q \]
- a) (i) \[\text{Work out the value of } H \text{ when } p=2,\; q=5.\] (2 marks)
- a) (ii) \[\text{Work out the value of } p \text{ when } H=30,\; q=4.\] (2 marks)
- b) \[\text{Work out the value of } H \text{ when } p=-1,\; q=7.\] (2 marks)
a) (i)
Answer:
\[ H=6(2)+3(5)=12+15=27.\]
Solution:
\[6(2)+3(5)=27.\]
a) (ii)
Answer:
\[ 30=6p+3(4)=6p+12 \implies 6p=18 \implies p=3.\]
Solution:
\[30=6p+12 \implies p=3.\]
b)
Answer:
\[ H=6(-1)+3(7)=-6+21=15.\]
Solution:
\[6(-1)+3(7)=-6+21=15.\]
6 marks
Foundation
Edexcel
Algebra
\[ J = 9u - 2v \]
- a) (i) \[\text{Work out the value of } J \text{ when } u=3,\; v=4.\] (2 marks)
- a) (ii) \[\text{Work out the value of } u \text{ when } J=25,\; v=2.\] (2 marks)
- b) \[\text{Work out the value of } J \text{ when } u=-2,\; v=5.\] (2 marks)
a) (i)
Answer:
\[ J=9(3)-2(4)=27-8=19.\]
Solution:
\[9(3)-2(4)=19.\]
a) (ii)
Answer:
\[ 25=9u-2(2)=9u-4 \implies 9u=29 \implies u=\tfrac{29}{9}.\]
Solution:
\[25=9u-4 \implies u=29/9.\]
b)
Answer:
\[ J=9(-2)-2(5)=-18-10=-28.\]
Solution:
\[9(-2)-2(5)=-28.\]
6 marks
Foundation
Edexcel
Algebra
\[ D = 2a - 3b \]
- a) (i) \[\text{Work out the value of } D \text{ when } a=5,\; b=2.\] (2 marks)
- a) (ii) \[\text{Work out the value of } a \text{ when } D=13,\; b=1.\] (2 marks)
- b) \[\text{Work out the value of } D \text{ when } a=-4,\; b=3.\] (2 marks)
a) (i)
Answer:
\[ D=2(5)-3(2)=10-6=4.\]
Solution:
\[2(5)-3(2)=10-6=4.\]
a) (ii)
Answer:
\[ 13=2a-3(1)=2a-3 \implies 2a=16 \implies a=8.\]
Solution:
\[13=2a-3 \implies 2a=16 \implies a=8.\]
b)
Answer:
\[ D=2(-4)-3(3)=-8-9=-17.\]
Solution:
\[2(-4)-3(3)=-8-9=-17.\]
6 marks
Foundation
Edexcel
Algebra
\[ B = 4p - 5q \]
- a) (i) \[\text{Work out the value of } B \text{ when } p=6,\; q=2.\] (2 marks)
- a) (ii) \[\text{Work out the value of } p \text{ when } B=27,\; q=1.\] (2 marks)
- b) \[\text{Work out the value of } B \text{ when } p=-3,\; q=4.\] (2 marks)
a) (i)
Answer:
\[ B=4(6)-5(2)=24-10=14.\]
Solution:
\[4(6)-5(2)=24-10=14.\]
a) (ii)
Answer:
\[ 27=4p-5(1)=4p-5 \implies 4p=32 \implies p=8.\]
Solution:
\[27=4p-5 \implies 4p=32 \implies p=8.\]
b)
Answer:
\[ B=4(-3)-5(4)=-12-20=-32.\]
Solution:
\[4(-3)-5(4)=-12-20=-32.\]
6 marks
Foundation
Edexcel
Algebra
\[ C = 5m + n \]
- a) (i) \[\text{Work out the value of } C \text{ when } m=2,\; n=7.\] (2 marks)
- a) (ii) \[\text{Work out the value of } m \text{ when } C=22,\; n=2.\] (2 marks)
- b) \[\text{Work out the value of } C \text{ when } m=-1,\; n=4.\] (2 marks)
a) (i)
Answer:
\[ C=5(2)+7=10+7=17.\]
Solution:
\[5(2)+7=10+7=17.\]
a) (ii)
Answer:
\[ 22=5m+2 \implies 5m=20 \implies m=4.\]
Solution:
\[22=5m+2 \implies 5m=20 \implies m=4.\]
b)
Answer:
\[ C=5(-1)+4=-5+4=-1.\]
Solution:
\[5(-1)+4=-5+4=-1.\]
6 marks
Foundation
Edexcel
Algebra
\[ E = 7k + 2m \]
- a) (i) \[\text{Work out the value of } E \text{ when } k=2,\; m=4.\] (2 marks)
- a) (ii) \[\text{Work out the value of } k \text{ when } E=36,\; m=1.\] (2 marks)
- b) \[\text{Work out the value of } E \text{ when } k=-1,\; m=5.\] (2 marks)
a) (i)
Answer:
\[ E=7(2)+2(4)=14+8=22.\]
Solution:
\[7(2)+2(4)=14+8=22.\]
a) (ii)
Answer:
\[ 36=7k+2(1)=7k+2 \implies 7k=34 \implies k=\tfrac{34}{7}.\]
Solution:
\[36=7k+2 \implies 7k=34 \implies k=34/7.\]
b)
Answer:
\[ E=7(-1)+2(5)=-7+10=3.\]
Solution:
\[7(-1)+2(5)=-7+10=3.\]
6 marks
Foundation
Edexcel
Algebra
\[ A = 3x + 2y \]
- a) (i) \[\text{Work out the value of } A \text{ when } x=4,\; y=6.\] (2 marks)
- a) (ii) \[\text{Work out the value of } x \text{ when } A=30,\; y=5.\] (2 marks)
- b) \[\text{Work out the value of } A \text{ when } x=-2,\; y=7.\] (2 marks)
a) (i)
Answer:
\[ A = 3(4) + 2(6) = 12 + 12 = 24 \]
Solution:
\[3(4)+2(6)=12+12=24.\]
a) (ii)
Answer:
\[ 30 = 3x + 2(5) = 3x+10 \Rightarrow 3x=20 \Rightarrow x=\tfrac{20}{3}.\]
Solution:
\[30=3x+10 \implies 3x=20 \implies x=20/3.\]
b)
Answer:
\[ A=3(-2)+2(7)=-6+14=8.\]
Solution:
\[3(-2)+2(7)=-6+14=8.\]