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Grade 11Common Core (CCSS) · Math

Aligned with the Common Core State Standards · All grades

Math · Grade 11

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Mixed review of all areas · Grade 11

Name: ____________________

Worked examples

Polynomial equations

  1. x³ = a: take the cube root of both sides.
  2. x³ = kx: move everything to one side and factor out x, so x = 0 is one solution.
  3. (x − a)(x − b)(x − c) = 0: the zero-product property gives x = a, x = b and x = c.

Quadratic functions and zeros

  1. Find two numbers whose sum and product match the coefficients: write (x − a)(x − b).
  2. The zeros are x = a and x = b.
  3. Example: x² − 5x + 6 = (x − 2)(x − 3), so x = 2 and x = 3.

Exponential growth and decay

  1. The growth factor is 1 + p/100 (or 1 − p/100 for a decrease).
  2. Multiply the start value by the factor to the power of the years.
  3. Example: 1,000 · 1.05³ ≈ 1,158.

Triangle area, sine and cosine rules

  1. Area: A = ½ · a · b · sin C.
  2. Cosine rule: c² = a² + b² − 2ab · cos C.
  3. Sine rule: a / sin A = b / sin B, so b = a · sin B / sin A.

Logarithms

  1. log_b(n) asks: which power of b gives n?
  2. Write n as a power of b.
  3. Example: log₂(8) = 3 because 2³ = 8.

Arithmetic sequences

  1. Each term grows by d.
  2. aₙ = a₁ + (n − 1)·d; sum = n·(a₁ + aₙ)/2.
  3. Example: a₁ = 3, d = 4 gives a₁₀ = 3 + 9·4 = 39.

Trigonometry in right triangles

  1. sin v = opposite/hypotenuse, cos v = adjacent/hypotenuse.
  2. Multiply the hypotenuse by sin v or cos v.
  3. Example: 10 · sin 30° = 5 cm.

Interest and percentage points

  1. The goal: work out how much money grows with interest – the interest or the new amount.
  2. Interest = capital × rate. Example: 2,000 kr in an account with 5% interest.
  3. After one year: 2,000 × 0.05 = 100 kr interest. Total: 2,100 kr.
  4. Compound interest, year two: 2,100 × 0.05 = 105 kr. Total: 2,205 kr.
  5. Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓

Inequalities

  1. Solve like an equation: move terms and divide.
  2. Dividing by a negative number flips the inequality.
  3. Example: 5 − 2x > 11 gives −2x > 6, so x < −3.

Statistics: mean, median and standard deviation

  1. Mean = sum / count. Median = middle value when sorted.
  2. Range = largest − smallest.
  3. Standard deviation: square each deviation from the mean, average them and take the square root.
1.

Solve: x³ = 49x

2.

Find the zeros: y = x² − 12x + 32

3.

The model for fund value uses amounts in kr. Find the value: 1000 grows by 14 % per year for 3 years (whole number) Answer with the correct unit.

4.

Find the third side (cosine rule): sides 18 cm and 9 cm, angle between them 114° (1 decimal)

5.

Solve: 10ˣ = 493 (2 decimals)

6.

The plan counts seats per row. The first amount is a₁ and the increase is d. Find the term: a₁ = 15, d = 6. a₂₈ = ? Answer with the correct unit.

7.

A roof model is shaped like a right triangle. Find the opposite side: hypotenuse 39 cm, angle 23° (1 decimal) Answer with the correct unit.

8.

The interest rate rises from 3.5 % to 5 %. How many percentage points is the increase?

9.

Solve: x³ = 16x

10.

Solve: 3x + 2 > -16

11.

The model for savings uses amounts in kr. Find the value: 20,000 grows by 7 % per year for 3 years (whole number) Answer with the correct unit.

12.

Find the range and median: 48, 11, 41, 33, 16, 23

13.

Solve: 10ˣ = 219 (2 decimals)

14.

Solve: 5x + 1 > 1

15.

Find the adjacent side: hypotenuse 38 cm, angle 52° (1 decimal)

16.

Solve: x³ = 9x

17.

Solve: x³ = 16x

18.

Find the value: 2000 grows by 12 % per year for 7 years (whole number)

19.

The model for equipment value uses amounts in kr. Find the value: 5000 decreases by 10 % per year for 9 years (whole number) Answer with the correct unit.

20.

Find the value: 5000 decreases by 4 % per year for 6 years (whole number)

Answer key

  1. 1. x = -7, x = 0, x = 7
  2. 2. x = 4, x = 8
  3. 3. 1482 kr
  4. 4. 23.2 cm
  5. 5. x ≈ 2.69
  6. 6. 177 seats
  7. 7. 15.2 cm
  8. 8. 1.5 percentage points
  9. 9. x = -4, x = 0, x = 4
  10. 10. x > -6
  11. 11. 24,501 kr
  12. 12. 37; median 28
  13. 13. x ≈ 2.34
  14. 14. x > 0
  15. 15. 23.4 cm
  16. 16. x = -3, x = 0, x = 3
  17. 17. x = -4, x = 0, x = 4
  18. 18. 4421
  19. 19. 1937 kr
  20. 20. 3914

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Grade
11 (ages 16–17)
Difficulty
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Number of tasks
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Task format
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More sheets for grade 11: Quadratic functions · Polynomial equations · Systems of equations · Inequalities · Exponential functions · Logarithms · Interest & percent change · Sequences · Statistics · Trigonometry · Sine & cosine rules · Equation of a circle

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  1. 1. Quadratic functions
  2. 2. Polynomial equations
  3. 3. Systems of equations
  4. 4. Inequalities
  5. 5. Exponential functions
  6. 6. Logarithms
  7. 7. Interest & percent change
  8. 8. Sequences
  9. 9. Statistics
  10. 10. Trigonometry
  11. 11. Sine & cosine rules
  12. 12. Equation of a circle
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