Daily Practice · Higher Plus
January 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1995 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1995A cuboid measures 7 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd January 1995A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd January 1995A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 4th January 1995A rectangle is 4 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th January 1995Work out the coordinates of the turning point of y = x^2 + 14x + 10.
- 6th January 1995y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 49.
- 7th January 1995The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 8th January 1995A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 9th January 1995On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th January 1995Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 11th January 1995Simplify (x^2 - 5x + 6)/(x - 3).
- 12th January 1995A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 13th January 1995In 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.
- 14th January 1995The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 15th January 1995A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 16th January 1995A block has mass 600 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.
- 17th January 1995In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 18th January 1995y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 19th January 1995In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?
- 20th January 1995A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 21st January 1995On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd January 1995x = 61 and y = 30, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd January 1995Make x the subject of 6x + 4 = y(x + 4).
- 24th January 1995y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 25th January 1995A cuboid measures 3 cm by 7 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th January 1995A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th January 1995A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 28th January 1995A car covers 420 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.
- 29th January 1995Write 2/(x - 2) + 2/(x - 4) as a single fraction.
- 30th January 1995y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 49.
- 31st January 1995A cuboid measures 8 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.