Daily Practice · Higher Plus
January 1997 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1997A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd January 1997In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 3rd January 1997The probability of winning a game is 1/2. A player expects 60 wins. How many games did they play?
- 4th January 1997A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 5th January 1997x = 95 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th January 1997Make x the subject of 7x + 5 = y(x + 5).
- 7th January 1997y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 8th January 1997In a vector proof you find that vector PQ = 3a - 5b and vector RS = 9a - 15b. What does this show about PQ and RS?
- 9th January 1997A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 10th January 1997On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th January 1997A car covers 150 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th January 1997Write 6/(x + 6) + 3/(x - 2) as a single fraction.
- 13th January 1997y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 14th January 1997A cuboid measures 4 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th January 1997A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th January 1997A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 17th January 1997Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 18th January 1997Solve 8x^2 + 6x + 1 = 0.
- 19th January 1997y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 16.
- 20th January 1997A cuboid measures 5 cm by 12 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st January 1997A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd January 1997On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd January 1997Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 24th January 1997f(x) = 3x - 8. Work out the inverse function f^-1(x).
- 25th January 1997A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 26th January 1997The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 27th January 1997A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 28th January 1997A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 29th January 1997A rectangle is 12 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th January 1997Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 31st January 1997y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.