Daily Practice · Higher Plus
December 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1990On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd December 1990x = 106 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd December 1990f(x) = 5x + 7. Work out the inverse function f^-1(x).
- 4th December 1990y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 5th December 1990In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 6th December 1990The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 7th December 1990A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 8th December 1990A car covers 710 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th December 1990Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 10th December 1990y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 9.
- 11th December 1990In a vector proof you find that vector PQ = a + 2b and vector RS = 2a + 4b. What does this show about PQ and RS?
- 12th December 1990A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 13th December 1990On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th December 1990Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 15th December 1990Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 16th December 1990A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 17th December 1990A cuboid measures 13 cm by 9 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th December 1990A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th December 1990A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 20th December 1990Simplify sqrt(48) + sqrt(75), giving your answer in the form a sqrt(b).
- 21st December 1990Work out the nth term of the quadratic sequence 2, 9, 22, 41, ...
- 22nd December 1990y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 23rd December 1990A cuboid measures 11 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th December 1990A bag holds 3 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th December 1990On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th December 1990A rectangle is 7 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th December 1990The point (-3, 3) lies on y = f(x). Write down its image on y = f(x) + 3.
- 28th December 1990y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 29th December 1990The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 30th December 1990A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 31st December 1990A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?