Daily Practice · Higher Plus
December 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2002A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 2nd December 2002In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 3rd December 2002The probability of winning a game is 1/5. A player expects 28 wins. How many games did they play?
- 4th December 2002A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 5th December 2002Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
- 6th December 2002f(x) = 6x - 1. Work out the inverse function f^-1(x).
- 7th December 2002y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 8th December 2002In a vector proof you find that vector PQ = a + b and vector RS = 4a + 4b. What does this show about PQ and RS?
- 9th December 2002A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 10th December 2002On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th December 2002A rectangle is 9 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th December 2002Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 13th December 2002y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 14th December 2002A cuboid measures 6 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th December 2002A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th December 2002A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 17th December 2002Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 18th December 2002Use the iteration x(n+1) = cube root of (12x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 19th December 2002y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 81.
- 20th December 2002A cuboid measures 9 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st December 2002A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd December 2002On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd December 2002A block has mass 260 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th December 2002Work out the nth term of the quadratic sequence -2, 8, 24, 46, ...
- 25th December 2002A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 26th December 2002The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 27th December 2002A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 28th December 2002A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 29th December 2002x = 43 and y = 30, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th December 2002The point (4, 2) lies on y = f(x). Write down its image on y = -f(x).
- 31st December 2002y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.