Daily Practice · Higher Plus
December 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1994y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 2nd December 1994A cuboid measures 13 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd December 1994A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th December 1994On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th December 1994A block has mass 720 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th December 1994f(x) = 5x - 6 and g(x) = 5x - 8. Work out fg(-2).
- 7th December 1994y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 8th December 1994The 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.
- 9th December 1994A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 10th December 1994A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 11th December 1994x = 186 and y = 126, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th December 1994The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 13th December 1994y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
- 14th December 1994In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 15th December 1994The probability of winning a game is 7/8. A player expects 49 wins. How many games did they play?
- 16th December 1994On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th December 1994A car covers 390 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th December 1994A quadratic sequence starts 12, 31, 60, 99. Work out the second difference, and the coefficient of n^2.
- 19th December 1994A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 20th December 1994In a vector proof you find that vector PQ = 3a - b and vector RS = 6a - 2b. What does this show about PQ and RS?
- 21st December 1994A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 22nd December 1994A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 23rd December 1994Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 24th December 1994Solve x^2 + 2x - 8 > 0.
- 25th December 1994y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 26th December 1994A cuboid measures 5 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th December 1994A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th December 1994On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th December 1994Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 30th December 1994Write x^2 + 4x + 3 in the form (x + a)^2 + b.
- 31st December 1994y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.