Daily Practice · Higher Plus
December 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1997A block has mass 780 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd December 1997Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 3rd December 1997A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 4th December 1997In a vector proof you find that vector PQ = 5a - 5b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 5th December 1997A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 6th December 1997A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 7th December 1997x = 97 and y = 63, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th December 1997Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 9th December 1997y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 10th December 1997A cuboid measures 8 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th December 1997A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th December 1997On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th December 1997A car covers 190 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th December 1997Work out the nth term of the quadratic sequence -1, 6, 17, 32, ...
- 15th December 1997y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 16th December 1997A cuboid measures 7 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th December 1997A bag holds 5 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th December 1997A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 19th December 1997Rationalise the denominator of 66/sqrt(11), giving your answer in its simplest form.
- 20th December 1997The point (-1, -5) lies on y = f(x). Write down its image on y = f(x - 5).
- 21st December 1997y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 22nd December 1997The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 23rd December 1997A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 24th December 1997On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th December 1997Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
- 26th December 1997Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 27th December 1997A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 28th December 1997In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 29th December 1997The probability of winning a game is 5/8. A player expects 35 wins. How many games did they play?
- 30th December 1997A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 31st December 1997A rectangle is 23 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.