Daily Practice · Higher Plus
August 1995 - Higher Plus 5-a-day
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The batch download puts all 5 tiers' August 1995 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1995On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd August 1995A rectangle is 24 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd August 1995Simplify (x^2 + 11x + 28)/(x + 7).
- 4th August 1995y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 5th August 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.
- 6th August 1995A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 7th August 1995A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 8th August 1995Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 9th August 1995In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 6 in terms of an integer n?
- 10th August 1995y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 64.
- 11th August 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.
- 12th August 1995The probability of winning a game is 1/2. A player expects 70 wins. How many games did they play?
- 13th August 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?
- 14th August 1995A block has mass 860 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.
- 15th August 1995Make x the subject of 4x + 7 = y(x + 7).
- 16th August 1995A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 17th August 1995In a vector proof you find that vector PQ = 6a - 5b and vector RS = 24a - 20b. What does this show about PQ and RS?
- 18th August 1995A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 19th August 1995A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 20th August 1995x = 196 and y = 27, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st August 1995Write 5/(x + 5) + 4/(x + 4) as a single fraction.
- 22nd August 1995y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 23rd August 1995A cuboid measures 13 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th August 1995A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th August 1995On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th August 1995A car covers 120 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.
- 27th August 1995Solve 4x^2 + 19x + 12 = 0.
- 28th August 1995y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 29th August 1995A cuboid measures 5 cm by 11 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th August 1995A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st August 1995A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?