Daily Practice · Higher Plus
December 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1989Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 2nd December 1989The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 3rd December 1989y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 4th December 1989The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 5th December 1989A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 6th December 1989On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th December 1989Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 8th December 1989A quadratic sequence starts 10, 28, 56, 94. Work out the second difference, and the coefficient of n^2.
- 9th December 1989y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 10th December 1989In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 11th December 1989The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 12th December 1989A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 13th December 1989A rectangle is 5 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th December 1989Solve x^2 - 4x - 12 < 0.
- 15th December 1989y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 81.
- 16th December 1989In a vector proof you find that vector PQ = a + 5b and vector RS = 3a + 15b. What does this show about PQ and RS?
- 17th December 1989A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 18th December 1989On 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?
- 19th December 1989Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 20th December 1989Write x^2 + 6x - 11 in the form (x + a)^2 + b.
- 21st December 1989A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 22nd December 1989A cuboid measures 11 cm by 6 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd December 1989A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th December 1989A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 25th December 1989A block has mass 550 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.
- 26th December 1989Work out the coordinates of the turning point of y = x^2 - 14x + 5.
- 27th December 1989y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 28th December 1989A cuboid measures 11 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th December 1989A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th December 1989On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 31st December 1989x = 138 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.