Daily Practice · Higher Plus
February 1995 - Higher Plus 5-a-day
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The batch download puts all 5 tiers' February 1995 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1995A bag holds 3 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd February 1995On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd February 1995Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 4th February 1995Solve 6x^2 - 25x + 25 = 0.
- 5th February 1995A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 6th February 1995The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 7th February 1995A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 8th February 1995A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 9th February 1995Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 10th February 1995f(x) = 4x + 1. Work out the inverse function f^-1(x).
- 11th February 1995y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 12th February 1995In 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.
- 13th February 1995The probability of winning a game is 3/5. A player expects 24 wins. How many games did they play?
- 14th February 1995On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th February 1995A rectangle is 24 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th February 1995Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 17th February 1995y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 18th February 1995In a vector proof you find that vector PQ = 4a + 3b and vector RS = 12a + 9b. What does this show about PQ and RS?
- 19th February 1995A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 20th February 1995A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 21st February 1995Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 22nd February 1995Use the iteration x(n+1) = cube root of (11x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 23rd February 1995y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 16.
- 24th February 1995A cuboid measures 7 cm by 9 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th February 1995A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th February 1995On 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?
- 27th February 1995A block has mass 660 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th February 1995Work out the nth term of the quadratic sequence 3, 16, 37, 66, ...