Daily Practice · Higher Plus
December 1987 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1987The point (-5, 4) lies on y = f(x). Write down its image on y = f(x) + 4.
- 2nd December 1987y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 3rd December 1987A cuboid measures 8 cm by 11 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th December 1987A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th December 1987On 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?
- 6th December 1987x = 200 and y = 158, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th December 1987Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 8th December 1987A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 9th December 1987A cuboid measures 4 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th December 1987A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th December 1987A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 12th December 1987A car covers 840 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th December 1987f(x) = 2x + 3 and g(x) = 6x + 9. Work out fg(0).
- 14th December 1987y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 15th December 1987The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 16th December 1987A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 17th December 1987On 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?
- 18th December 1987Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 19th December 1987The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 20th December 1987y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 21st December 1987In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 22nd December 1987The probability of winning a game is 9/10. A player expects 54 wins. How many games did they play?
- 23rd December 1987A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 24th December 1987Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 25th December 1987A quadratic sequence starts -3, 3, 13, 27. Work out the second difference, and the coefficient of n^2.
- 26th December 1987y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 81.
- 27th December 1987In a vector proof you find that vector PQ = 4a - 6b and vector RS = 16a - 24b. What does this show about PQ and RS?
- 28th December 1987A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 29th December 1987On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th December 1987A rectangle is 6 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st December 1987Solve x^2 + 4x + 3 > 0.