Original unit assessment covering the skills listed below. This is not an official past paper or a complete qualification mock. Suggested time is a guide, not an exam-board requirement.
45 minutes · 45 marks
Name: ____________________ · Date: ____________
1. Solve over the real numbers: x² + (-5)x + (-66) = 0. Give every distinct root. (3 marks)
2. Solve over the real numbers: x² + (-4)x + (-77) = 0. Give every distinct root. (3 marks)
3. Solve over the real numbers: x² + (-3)x + (-18) = 0. Give every distinct root. (3 marks)
4. Solve over the real numbers: x² + (-18)x + (72) = 0. Give every distinct root. (3 marks)
5. Solve over the real numbers: x² + (-2)x + (-8) = 0. Give every distinct root. (3 marks)
WorksheetWise · Standard · 1097
Practice assessment · Advanced mathematics
Original unit assessment covering the skills listed below. This is not an official past paper or a complete qualification mock. Suggested time is a guide, not an exam-board requirement.
Original unit assessment covering the skills listed below. This is not an official past paper or a complete qualification mock. Suggested time is a guide, not an exam-board requirement.
45 minutes · 45 marks
Name: ____________________ · Date: ____________
11. Find an indefinite integral of 40 x^4 + (7) with respect to x. Include the constant of integration. (3 marks)
12. Find an indefinite integral of 25 x^4 + (-12) with respect to x. Include the constant of integration. (3 marks)
13. Find an indefinite integral of 21 x^2 + (-3) with respect to x. Include the constant of integration. (3 marks)
14. Find an indefinite integral of 45 x^4 + (12) with respect to x. Include the constant of integration. (3 marks)
15. Find an indefinite integral of 36 x^5 + (7) with respect to x. Include the constant of integration. (3 marks)
WorksheetWise · Standard · 1097
Practice assessment · Advanced mathematics — Answer key
Original unit assessment covering the skills listed below. This is not an official past paper or a complete qualification mock. Suggested time is a guide, not an exam-board requirement.
45 minutes · 45 marks
1. Solve over the real numbers: x² + (-5)x + (-66) = 0. Give every distinct root. (3 marks)
x = -6; x = 11
x² + (-5)x + (-66) = (x − (-6))(x − (11)). Set each factor equal to zero.
2. Solve over the real numbers: x² + (-4)x + (-77) = 0. Give every distinct root. (3 marks)
x = -7; x = 11
x² + (-4)x + (-77) = (x − (-7))(x − (11)). Set each factor equal to zero.
3. Solve over the real numbers: x² + (-3)x + (-18) = 0. Give every distinct root. (3 marks)
x = 6; x = -3
x² + (-3)x + (-18) = (x − (6))(x − (-3)). Set each factor equal to zero.
4. Solve over the real numbers: x² + (-18)x + (72) = 0. Give every distinct root. (3 marks)
x = 12; x = 6
x² + (-18)x + (72) = (x − (12))(x − (6)). Set each factor equal to zero.
5. Solve over the real numbers: x² + (-2)x + (-8) = 0. Give every distinct root. (3 marks)
x = 4; x = -2
x² + (-2)x + (-8) = (x − (4))(x − (-2)). Set each factor equal to zero.
WorksheetWise · Standard · 1097
Practice assessment · Advanced mathematics — Answer key
Original unit assessment covering the skills listed below. This is not an official past paper or a complete qualification mock. Suggested time is a guide, not an exam-board requirement.
45 minutes · 45 marks
6. For f(x) = 5 x^5 + (-7), find f′(x). (3 marks)
25 x^4
Power rule: d(x^n)/dx = n x^(n−1). A constant differentiates to 0.
7. For f(x) = 6 x^2 + (-2), find f′(x). (3 marks)
12 x^1
Power rule: d(x^n)/dx = n x^(n−1). A constant differentiates to 0.
8. For f(x) = 1 x^5 + (6), find f′(x). (3 marks)
5 x^4
Power rule: d(x^n)/dx = n x^(n−1). A constant differentiates to 0.
9. For f(x) = 2 x^2 + (-6), find f′(x). (3 marks)
4 x^1
Power rule: d(x^n)/dx = n x^(n−1). A constant differentiates to 0.
Power rule: d(x^n)/dx = n x^(n−1). A constant differentiates to 0.
WorksheetWise · Standard · 1097
Practice assessment · Advanced mathematics — Answer key
Original unit assessment covering the skills listed below. This is not an official past paper or a complete qualification mock. Suggested time is a guide, not an exam-board requirement.
45 minutes · 45 marks
11. Find an indefinite integral of 40 x^4 + (7) with respect to x. Include the constant of integration. (3 marks)
8 x^5 + (7)x + C
Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.
12. Find an indefinite integral of 25 x^4 + (-12) with respect to x. Include the constant of integration. (3 marks)
5 x^5 + (-12)x + C
Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.
13. Find an indefinite integral of 21 x^2 + (-3) with respect to x. Include the constant of integration. (3 marks)
7 x^3 + (-3)x + C
Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.
14. Find an indefinite integral of 45 x^4 + (12) with respect to x. Include the constant of integration. (3 marks)
9 x^5 + (12)x + C
Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.
15. Find an indefinite integral of 36 x^5 + (7) with respect to x. Include the constant of integration. (3 marks)
6 x^6 + (7)x + C
Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.
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