Daily Practice · Higher Plus
December 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1992A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 2nd December 1992On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd December 1992Simplify sqrt(50) + sqrt(98), giving your answer in the form a sqrt(b).
- 4th December 1992Work out the nth term of the quadratic sequence 6, 15, 32, 57, ...
- 5th December 1992A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 6th December 1992A cuboid measures 11 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th December 1992A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th December 1992A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 9th December 1992A rectangle is 20 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th December 1992The point (6, -2) lies on y = f(x). Write down its image on y = f(x - 4).
- 11th December 1992y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 12th December 1992A cuboid measures 7 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th December 1992A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th December 1992On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th December 1992Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 16th December 1992Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 17th December 1992y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 18th December 1992The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 19th December 1992A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 20th December 1992A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 21st December 1992A block has mass 730 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd December 1992f(x) = 5x - 1 and g(x) = 4x - 3. Work out fg(2).
- 23rd December 1992y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 9.
- 24th December 1992In 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.
- 25th December 1992The probability of winning a game is 1/5. A player expects 12 wins. How many games did they play?
- 26th December 1992On 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?
- 27th December 1992x = 81 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th December 1992The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 29th December 1992A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 30th December 1992In a vector proof you find that vector PQ = 6a - 2b and vector RS = 18a - 6b. What does this show about PQ and RS?
- 31st December 1992A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.