Daily Practice · Higher Plus
November 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1995 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1995Write x^2 - 8x + 4 in the form (x + a)^2 + b.
- 2nd November 1995y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 3rd November 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.
- 4th November 1995A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 5th November 1995On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th November 1995A block has mass 880 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.
- 7th November 1995Work out the coordinates of the turning point of y = x^2 + 16x + 7.
- 8th November 1995y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 9th November 1995In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 10th November 1995The probability of winning a game is 3/4. A player expects 21 wins. How many games did they play?
- 11th November 1995A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 12th November 1995x = 92 and y = 27, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th November 1995Simplify (x^2 - x - 30)/(x - 6).
- 14th November 1995y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 36.
- 15th November 1995In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
- 16th November 1995A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 17th November 1995On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th November 1995A car covers 400 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th November 1995In an algebraic proof, how would you write an even number in terms of an integer n?
- 20th November 1995A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 21st November 1995A cuboid measures 8 cm by 13 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd November 1995A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd November 1995A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 24th November 1995Rationalise the denominator of 21/sqrt(3), giving your answer in its simplest form.
- 25th November 1995Make x the subject of 8x + 2 = y(x + 2).
- 26th November 1995y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 27th November 1995A cuboid measures 4 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th November 1995A bag holds 5 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th November 1995On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th November 1995Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).